Thermodynamic Approach for Co-crystal Screening | Crystal Growth

Article pubs.acs.org/crystal

Cite This: Cryst. Growth Des. 2019, 19, 3253−3264

Thermodynamic Approach for Co-crystal Screening Heiner Veith,† Miko Schleinitz,† Carsten Schauerte,‡ and Gabriele Sadowski*,† †

Department of Chemical and Biochemical Engineering, Laboratory of Thermodynamics, TU Dortmund University, Emil-Figge-Str. 70, D-44227 Dortmund, Germany ‡ solid-chem GmbH, Universitätsstr. 136, D-44799 Bochum, Germany

Downloaded via UNIV OF SOUTHERN INDIANA on July 24, 2019 at 11:38:39 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

S Supporting Information *

ABSTRACT: Co-crystallization is a promising strategy to enhance the water solubility and bioavailability of active pharmaceutical ingredients (APIs). Once possible coformers have been identified, suitable process conditions for an effective generation of pure co-crystals have to be found. In this work, two screening approaches have been developed to find the best-suited solvent and optimum process conditions for co-crystal formation: a shortcut approach based on mass balances and a second one which additionally accounts for thermodynamic nonidealities between the API, the coformer, and the solvent via the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT). The enhanced efficiency of the two approaches compared to conventional ones is demonstrated for the two co-crystal-forming systems carbamazepine/ acetylsalicylic acid and carbamazepine/salicylic acid. Appropriate conditions for co-crystal formation were identified in the solvents ethanol, ethyl acetate, acetonitrile, and methanol using the novel screening approaches. Phase diagrams were predicted using PC-SAFT and validated by experiments. It will be shown that the co-crystal screening approach based on thermodynamic predictions yields an appropriate preselection of suitable solvents and thus can be used to determine best-performing solvents for co-crystal production with minimal experimental effort.

1. INTRODUCTION The average time for research and development of an active pharmaceutical ingredient (API) takes on the order of a decade, or more, with some exceptions.1 Within this period of time, the initial research focuses on the molecular structure and the resulting therapeutic effect of the API, whereas the solidstate form of the API for optimal physical properties, such as solubility, dissolution, stability, etc., is investigated at later stages of development. 2 A major challenge for the pharmaceutical industry is the often low solubility of APIs in water: 40% of the marketed APIs and even 80−90% of the APIs in development suffer from a low aqueous solubility.3,4 Possibilities to overcome solubility limitations are the production of different crystalline forms, such as polymorphs, salts, solvates, hydrates, or co-crystals (CC).2 CCs are crystalline materials composed of an API and a coformer (CF) in a stoichiometric ratio.5 Different in silico approaches have been established to identify suitable coformers.6−14 Afterward, CC formation with these coformers needs to be verified experimentally in a CC screening. The latter is usually performed via different crystallization techniques, such as dry grinding, solvent drop grinding,2 cooling crystallization, or slurry crystallization, which compares to solvent crystallization15−17 or reaction crystallization.18−20 In a CC screening using slurry crystallization, a saturated mixture of API, CF, and solvent with excess solute is equilibrated for a long time (e.g., 48 h) to ensure that the thermodynamically most-stable crystalline form, preferably the © 2019 American Chemical Society

CC, will prevail. After the equilibrium is reached, analysis of the crystalline phase is performed to evaluate the CC formation. For CC screening using cooling crystallization, an unsaturated mixture of API, CF, and solvent is prepared at a high starting temperature. Afterward, supersaturation is induced through cooling of the solution to a lower end temperature. As soon as crystals appear, analysis of the crystalline phase is performed and the screening is evaluated. The outcome of screening experiments using both, slurry crystallization and cooling crystallization, depends on the screening composition of API, CF, and solvent. Thus, CCs might not be found in screenings starting from inappropriate screening compositions, although CCs would form at different screening compositions of the same mixture.21 However, finding the appropriate screening compositions for CC screening on a trial-and-error basis is quite time-consuming. Therefore, prior to the experiments, it is valuable to determine screening compositions of API/CF/solvent for which thermodynamically stable CCs are expected to crystallize. This information is available from thermodynamic phase diagrams. These phase diagrams for API/CF/solvent systems denote screening composition regions in which crystals of pure API or CF, or pure CCs are thermodynamically stable. However, determining these ternary phase diagrams requires a Received: January 22, 2019 Revised: March 18, 2019 Published: May 10, 2019 3253

DOI: 10.1021/acs.cgd.9b00103 Cryst. Growth Des. 2019, 19, 3253−3264

Crystal Growth & Design

Article

Figure 1. Schematic phase diagram for an API/coformer/solvent system (a) without co-crystal (CC) formation and (b) with formation of a 1:1 CC. Black dotted lines are the real-solubility lines of API and coformer (CF) in the ternary system. The CC solubility line is represented by the gray dotted line in Figure 1b. Dashed lines are hypothetical solubility lines providing constant solubility in the solvent without influence of the other solute on the solubility and assuming insoluble behavior in the other solute. L denotes the liquid phase; the eutectic points are shown as gray squares. The CC stoichiometric ratio in solution is presented as the dashed-dotted line in Figure 1b.

activity, at which the CC is more stable than the API crystal. Lange and Sadowski29 showed that the concentration window for CC formation in solvents and solvent mixtures can be predicted based only on one solubility data point of each API, CF, and CC in any solvent. While being very universally applicable and reliable, it does require extensive thermodynamic modeling. In this work, we now present a short-cut approach (SCA) to obtain suitable screening compositions for experimental CC screening in an API/CF/solvent system. This approach only requires the pure-component solubilities of API and CF in the selected solvent as well as the CC stoichiometry. The advantage of this approach is that it requires only very little experimental effort and does not require thermodynamic modeling. Second, we propose a thermodynamic approach (TA) to obtain a suitable screening composition that accounts for thermodynamic nonidealities in the API/CF/solvent system. Furthermore, this approach can be used to identify the best-suited solvent for CC generation based on predicted phase diagrams. The formation of CCs at screening compositions obtained from both approaches was successfully validated via slurry crystallization for the two CC systems carbamazepine (CBZ)/acetylsalicylic acid (ASA) and carbamazepine (CBZ)/salicylic acid (SA) and via cooling crystallization for the system CBZ/ASA.

huge effort as many experiments have to be performed and the compositions of the developing crystals as well as of the liquid phases have to be analyzed for each screening composition. Hong et al.22 proposed an approach to experimentally obtain the ternary phase diagrams without the need to analyze the crystalline phase but screening a wide range of screening compositions and analyzing the resulting liquid phases. Another approach is to obtain these phase diagrams by analyzing the equilibrated liquid and crystalline phases ones the eutectic points are known.23 However, the screening for these eutectic points still comprises an intensive experimental effort, as various screening compositions have to be prepared and analyzed. Therefore, different approaches have been developed to obtain appropriate compositions for the screening experiments. The simplest approach is to dissolve the API and the CF in the stoichiometric ratio of the desired CC in a common solvent.15,24 However, for many systems, this approach is not successful, as the required API/CF stoichiometric ratio in a solvent often differs from the API/CF stoichiometric ratio in the CC.21 This particularly applies to cases where the solubility of the CF in the common solvent is significantly higher or lower than that of the API (so-called incongruent solubility of API and CF). To account for those systems, the use of solvent mixtures that lead to congruent solubility has been proposed.25 Systems with incongruent solubility are often neglected,26 although they could be very helpful for CC screening if appropriate API/CF screening ratios would be applied. Furthermore, screening approaches have been developed, where the suitable screening compositions are found via adding one solute (API or CF) to the saturated solution of the other one until crystallization occurs.19,20 However, this screening might result in the simultaneous formation of crystal mixtures API/CC or CF/CC, although also pure CCs could be formed in these systems at other (more appropriate) screening compositions.21 The aforementioned approaches are completely empirical and do not account for the real solubility behavior of API and CF. However, depending on the system, the mutual influence on solubility of API and CF might be tremendous. To account for these nonidealities, thermodynamic activities of the solutes (API and CF) have to be considered.27−31 Zhang et al.32 used the thermodynamic activity of the CF to obtain the critical CF

2. THEORY 2.1. Ternary Phase Diagrams. A thermodynamic phase diagram is an important tool to find the screening composition region for the formation of pure CCs. The thermodynamic phase diagram for a ternary system API/CF/solvent is schematically shown in Figure 1. Figure 1a depicts a system without CC formation. API and CF are completely commonly dissolved in the solvent in region L. In the CF + L region, any screening solution will lead to a saturated solution L having a composition along the dotted solubility line which is in equilibrium with CF crystals. Similarly, screening compositions in the API + L region will result in saturated solutions with compositions along the dotted solubility line and are in equilibrium with API crystals. The solubility lines intersect at the eutectic point. The composition at this point is the composition of the saturated 3254



Article

2.3. PC-SAFT. PC-SAFT34,35 was used in this work in order to calculate the thermodynamic activity coefficients in eqs 1 and 3. It calculates the residual Helmholtz energy aresidual (eq 4) consisting of three contributions caused by hard-chain repulsion ahard‑chain, dispersive attractions via van der Waals forces adispersion, and association via hydrogen bonds aassociation.

liquid phase in equilibrium with both, API and CF crystals, for all compositions in the CF + API + L region. Figure 1b represents a system of API, CF, and solvent, in which CC formation occurs. The regions L, CF + L, and API + L are defined in the same way as in Figure 1a. The region CC + L is best-suited for CC formation since, for all screening compositions located in that region, saturated solutions of compositions along the gray-dotted line are in thermodynamic equilibrium with pure CCs. For screening compositions in the adjacent regions (CC + CF + L and CC + API + L), CCs are present in a physical mixture with crystals of either CF or API. The equilibrated saturated liquid is again the one of the respective eutectic points. It is worth mentioning that the region of pure CC formation (CC + L) is (as shown in Figure 1b) not symmetrically located in the middle of the phase diagram. Thus, API/CF screening ratios leading to pure CCs might have to be different from the expected stoichiometric ratio of the CC (see dashed-dotted line Figure 1b). 2.2. Solubility Calculations. In order to predict the solubility lines of API or CF in the ternary phase diagram, the thermodynamic equilibrium condition between a crystalline phase (pure API or CF) and the saturated-liquid phase has to be fulfilled according to eq 1:33 ÄÅ SL SL SL T yz ΔcP ,0i ijj T0i 1 ÅÅÅÅ Δh0i ijj jj jj1 − SL zzz − −1 xi = expÅÅ− z γi ÅÅÅ RT jk R jk T T 0 i { Ç ÉÑ T0SLi yzzÑÑÑÑ zzÑÑ − ln T z{ÑÑÑ (1) Ö

aresidual = ahard‐chain + adispersion + aassociation

All components described within PC-SAFT require at least three pure-component parameters, namely, the number of segments mseg, the segment diameter σi, and the dispersion energy ui/kB. Since every component investigated in this work forms hydrogen bonds, two additional pure-component parameters, namely, the association-energy εAiBi/kB and association-volume κAiBi, are used to account for these associative forces. Combining rules are used to describe the properties in mixtures of components i and j. The combining rules of Berthelot−Lorentz were applied for the segment diameter σij (eq 5) and dispersion-energy parameter ui/kB (eq 6) in mixtures. Combining rules of Wolbach and Sandler36 are used to calculate the association-energy parameter εAiBj/kB (eq 7) and the association-volume parameter κAiBj (eq 8) in mixtures. As shown in eq 6, a binary interaction parameter kij can be used to correct the calculated cross-dispersion-energy uij/kB. σij =

K s , CC

ε AiBj =

κ

∏ (xi·γi)ν

i

i

= (xAPI ·γAPI )νAPI ·(xCF ·γCF )νCF

(5)

AiBj

=

(6)

1 AiBi (ε + ε AjBj) 2

κ

i yz σσ i j zz jj z j (1/2)(σi + σj) zz k {

AiBi AjBj j jj

κ

(7) 3

(8)

2.4. Approaches for CC Screening. The developed approaches require the pure-component solubilities of API and CF in the solvent as well as the CC stoichiometric ratio for screening. If the stoichiometric ratio for screening is inaccessible, one screening composition according to this approach has to be prepared for each stoichiometric ratio. 2.4.1. Shortcut Approach. The shortcut approach (SCA) uses the experimentally determined pure-component solubilities of API and CF in the solvent (Figure 2, black squares) to approximate a phase diagram without CC formation. Assuming that the ratio of API to solvent does not depend on the amount of CF (and vice versa), the API and CF solubility in the ternary API/CF/solvent system would evolve along the gray dashed lines, respectively. The intersection of these so-obtained solubility lines (also neglecting CC formation) in the ternary phase diagram could be used as screening composition of the experimental CC screening (Figure 2, point III). However, as this point might be located close to or even outside the real CC solubility line (Figure 2), only very small amounts of the crystalline CC or even an unsaturated solution might be obtained after equilibration. Therefore, we propose to apply a mass balance between the intersection point III and the pure CC (Figure 2, point I) and to move the screening point (Figure 2, point II) along this mass-balance line. A lever ratio between 0 (equals the point I) and 1 (equals the intersection point III) is chosen to increase the amount of CC while safely

(2)

The equilibrium constant Ks,CC is the so-called solubility product and can be expressed by the component’s mole fraction xi, thermodynamic activity coefficients γi, and stoichiometric coefficients νi: Ks , CC =

1 (σi + σj) 2

uij = (1 − kij) uiuj

In this equation, xi is the mole fraction solubility of component i (API or CF) in the liquid phase, whereas ΔhSL 0i , SL TSL 0i , and ΔcP,0i are the melting enthalpy, melting temperature, and the difference in the heat capacities of crystalline and liquid component i, respectively. T is the system temperature, and R is the ideal gas constant (8.314 J (mol K)−1). γi is the thermodynamic activity coefficient of the component i in the liquid phase and depends on temperature and concentration of all components (solvent, API, and CF) in the liquid phase. It accounts for the thermodynamic nonideality of the ternary mixture and can be calculated from a thermodynamic model (in this work, PC-SAFT). The formation of a CC is treated as a chemical reaction of the API and CF (eq 2), where νAPI and νCF are the stoichiometric coefficients of API and CF in the CC. νAPI API + νCF CF ←→ ⎯ CC

(4)

(3)

It is important to note that the solubility product depends neither on the type nor on the concentration of the solvent. Thus, once the solubility product is known (e.g., from one CC solubility data point in any solvent), it can be used to predict the CC solubility in any other solvent or solvent mixture using the thermodynamic activity coefficients in that solvent(mixture).29 3255



Article

Figure 2. Scheme of the shortcut approach (SCA) requiring only the solubility of pure API and CF in the solvent (black squares) and the CC stoichiometry (white circle, I) to estimate the screening composition (gray circle, II). The real phase behavior is schematically depicted by black solid lines. The assumed eutectic point neglecting CC formation is depicted by a black circle (III). The dashed gray lines represent the solubility of each component in the solvent neglecting the influence of the other solute, and the dotted line corresponds to the mass balance to obtain the screening point (II).

Figure 3. Scheme of the thermodynamic approach (TA) with the predicted eutectic point neglecting CC formation (black circle, III) and CC stoichiometry (white circle, I) to determine the optimal screening composition for a screening experiment (gray circle, II). The real phase behavior of the system is depicted by black solid lines. The predicted solubility line without CC formation is represented by the gray dashed lines, and the dotted line corresponds to the mass balance to obtain the screening composition of the screening point II.

staying in the CC-formation region after equilibration: the lower the lever ratio, the closer point II is to point I and the higher is the mass of the CC formed. If the amount of crystals in the slurry or at the end of cooling crystallization is too high, values of the lever ratio greater than 1 can be chosen to lower the amount of crystals. As the SCA neglects thermodynamic nonidealities, it does not require any thermodynamic calculations. 2.4.2. Thermodynamic Approach. To increase the probability for successfully identifying the CC region compared to the SCA, a thermodynamic approach (TA) accounting for nonidealities in the API/CF/solvent mixture was developed. The two solubility lines of API and CF in the presence of the respective other component (CF or API) in the common solvent are now predicted using the solute thermodynamic activity coefficients obtained from PC-SAFT (eq 1). Although the predicted solubility lines might not perfectly fit the real ones (as shown in Figure 3), they do provide a more-realistic trend than the ideal-solubility lines shown in Figure 2 and will thus increase the chance of correctly locating the CC-formation region in the composition triangle. The location of the predicted eutectic point (neglecting the CC formation) in the system API/CF/solvent is then estimated as the intersection of the two predicted solubility lines. The higher the nonidealities in the ternary API/CF/ solvent system, the more the predicted eutectic point differs from the one obtained by the SCA (section 2.4.1). Using this predicted eutectic point III and the stoichiometric CC ratio, the screening composition of the screening point II is again chosen along a mass-balance line by adapting a lever ratio between 0 (pure CC) and 1 (predicted eutectic point) to allow for a slurry leading to an amount of crystals sufficient for solidstate form analysis.

CBZ/SA,19,39 form CCs with molar ratios of 1:1. Ethanol (99.8%), ethyl acetate (99.9%), acetonitrile (≥99.9%), and methanol (99.9%) were obtained from VWR Chemicals (Darmstadt, Germany). All components were used as obtained without further purification. 3.2. Slurry Crystallization for Co-crystal Screening. Defined screening compositions of API, CF, and solvent were mixed in a glass vial (2 mL). This vial was equipped with a magnetic stirrer, sealed, and placed in a temperature-controlled stainless-steel block. Preliminary tests revealed that the solubility equilibrium for the considered systems was reached within 48 h. Nevertheless, the samples were equilibrated for at least 5 days before sampling. Afterward, crystals were retrieved from the glass vial and dried on filter paper. The obtained crystal structure was analyzed using powder X-ray diffraction (PXRD) (Miniflex 600, Rigaku, Japan) in reflection mode with 2Θ increasing at a rate of 5° per minute. A tube voltage of 40 kV and an electric current of 15 mA with a Cu Kα anode was used to record the diffractogram between 2° and 60° in 2Θ in steps of 0.02°. 3.3. Cooling Crystallization for Co-crystal Screening. Defined screening compositions of CBZ, ASA, and the solvent were prepared in temperature-controlled glass vessels with a volume of 20 mL. The mixture was heated to 308.15 K to obtain unsaturated solutions. Afterward, constant cooling of 0.6 K min−1 was performed until the end temperature of 288.15 K. Sample preparation and analysis of the crystal were performed analogous to the slurry crystallization. 3.4. Solubility Measurements. The solubility of CBZ, ASA, and SA was measured in the solvents ethanol, ethyl acetate, acetonitrile, and methanol at 298.15 K. For that purpose, the solutes were added to the solvents in excess to generate saturated solutions with excess crystals. Solubility measurements were performed in temperaturecontrolled glass vessels with a volume of 20 mL.27,28 After at least 48 h of equilibrating, samples of the saturated liquid phase were taken using syringe filters (pore size 0.45 μm) to fully remove the crystalline phase. Concentrations of CBZ, ASA, and SA in the samples were determined gravimetrically (by evaporating the volatile solvent under vacuum conditions) for the pure-component solubilities. In the case of solubility measurements of a multisolute system, the solute concentrations in the saturated liquid were determined photometrically using a UV/VIS-spectroscope (Eppendorf BioSpectrometer, Hamburg, Germany). For this purpose, calibration curves in ethanol were determined for CBZ/ASA and mixtures thereof at 238 and 299 nm wavelength and for CBZ/SA and mixtures thereof at 238 and 271 nm. Using a linear system of equations obtained from the calibrations, the amount of API and CF can be obtained.

3. MATERIALS & METHODS 3.1. Materials. CBZ (purity 98%) was purchased as Form III crystals from Alfa Aesar (Karlsruhe, Germany). ASA (USP grade) and SA (purity ≥ 99%) were purchased as crystalline powders from Sigma-Aldrich (Hamburg, Germany). Both, CBZ/ASA37,38 and the 3256



Article

Table 1. Screening Compositions Obtained from the SCA Using the Stated Lever Ratios as Well as the Resulting Crystalline Phases Obtained from Slurry Crystallization at These Screening Compositions at T = 298 K for Eight Ternary Systems API/CF

solvent

wAPI [g g−1]

wCF [g g−1]

lever ratio

crystals

CBZ/ASA

ethanol ethyl acetate acetonitrile methanol ethanol ethyl acetate acetonitrile methanol

0.247 0.249 0.272 0.225 0.102 0.256 0.231 0.249

0.263 0.227 0.225 0.327 0.278 0.228 0.160 0.302

0.6 0.57 0.58 0.65 0.62 0.6 0.6 0.65

CC CC CC CC CC + SA CC CC CC + SA

CBZ/SA

Figure 4. Ternary phase diagrams of the system CBZ/ASA/ethanol in mass fractions at (a) 298.15 K and (b) 288.15 K including the screening compositions estimated from the SCA as gray star and the TA as black star for the (a) slurry crystallization and (b) cooling crystallization (screening points for SCA and TA overlap in (b)). The black lines are the modeled phase boundaries using PC-SAFT, and the CC region estimated from the TA is highlighted in gray. Thus, to obtain the solubility in the solvents ethyl acetate, acetonitrile, and methanol, the solvents were completely evaporated and the remaining crystals were diluted in ethanol for analysis. Each solubility point is the mean value out of three measurements. The crystal structure of the equilibrated crystalline phase was again analyzed by PXRD in order to check the resulting solid-state form. The analytic method was adapted from Lange et al.31

4. RESULTS AND DISCUSSION 4.1. Shortcut Approach. 4.1.1. Slurry Crystallization for Co-crystal Screening (SCA). The screening compositions determined by the SCA (see Figure 2) are summarized in Table 1. As an example, the SCA-determined screening composition for the system CBZ/ASA/ethanol can be seen in Figure 4a. It is worth noting that the SCA-determined ratio of API/CF for the screening compositions significantly differs from the CC stoichiometric ratio in solution. Slurries with these screening compositions were prepared for CBZ/ASA and CBZ/SA mixtures in ethanol, ethyl acetate, acetonitrile, and methanol. The resulting crystal phases can also be found in Table 1. CC formation was found for all SCA-determined screening compositions in the investigated systems. The formation of pure CBZ/ASA CCs was confirmed via PXRD measurements for each investigated solvent, namely, ethanol, ethyl acetate, acetonitrile, and methanol (as example shown in Figure 5). Pure CBZ/SA CCs were obtained in ethyl acetate and acetonitrile (example in Figure 6), and a mixture of CC and SA crystals was obtained in the solvents ethanol and methanol. It is worth noting that the proximity of the obtained screening composition to the phase border of the CC region (see Figure 4a) might result in the formation of the mixture of CC and CF crystals. Moreover, nonideal mixing in the slurry

Figure 5. (a) PXRD diffractogram of CBZ/ASA CC obtained from slurry crystallization at screening compositions obtained from the SCA and (b) the reference PXRD diffractogram derived from SCXRD data (TAZRAO) taken from the Cambridge Structural Database.40

might lead to insufficient dissolution of the CF, and thus, the thermodynamic equilibrium (in this case pure CC) might not have been reached. The formation of a crystal mixture might also mean that the obtained screening composition is not located in the CC region. Nevertheless, a diffractogram different from the ones of pure API or CF crystals still proves the formation of a solid-state form different from API or CF. Further investigations will be necessary to verify the formation of a CC. 4.1.2. Cooling Crystallization for Co-crystal Screening (SCA). Cooling crystallization can be used for CC screening as a time-efficient alternative to slurry crystallization. It is based in the same phase diagrams as shown in Figures 2 and 3. The only difference is that it does not work isothermally but 3257



Article

illustrated in Figure 4b. Screening via cooling crystallization was conducted for the system CBZ/ASA in each of the solvents ethanol, ethyl acetate, acetonitrile, and methanol from temperatures of 308.15−288.15 K in less than 40 min. CC formation was again observed for all investigated systems. Pure CBZ/ASA CCs were found in ethanol and acetonitrile for the screening compositions obtained from the SCA. In the other solvents, namely, ethyl acetate and methanol, CCs as well as ASA crystals were formed. Obviously, the formation of a pure CC is preferred to the formation of a mixture of CC and ASA crystals within the screening. Thus, the screening results for the slurry crystallization (pure CCs for six out of eight systems) seem to be better than those for the cooling crystallization (pure CCs for two out of four systems). A system with congruent solubility at the starting temperature might be incongruent at the end temperature (see Figure 7). As the SCA does only evaluate the pure-component solubilities at the end temperature, it does not consider the shifting of the CC region as a function of temperature, and therefore, SCA leads to less reliable results for screening compositions of CC cooling crystallization. Another disadvantage of the cooling crystallization compared to the slurry crystallization for CC screening is that nucleation and crystal growth is kinetically inhibited, and thus, crystals might not form during the short time period of the experiment. The significant advantage of this screening approach is the short time effort for the screening experiment, as long as crystallization takes place. This way, the screening experiment can be shortened to less than 1 h compared to at least 48 h of equilibrating in the slurry screening experiments. The SCA proved to be a simple and reliable approach to generate suitable screening compositions for the slurry as well as the cooling crystallization to evaluate the CC formation without the need of thermodynamic calculations. However, the obtained screening composition might not be suitable for systems with highly nonideal thermodynamic behavior. 4.2. Thermodynamic Approach. 4.2.1. PC-SAFT Parameters. The TA considers the nonideal thermodynamic behavior of the systems via the thermodynamic model PC-SAFT (see section 2.3). The PC-SAFT pure-component parameters of the considered compounds were taken from the literature29,34,35,41−43 and are summarized in Table 3. Additionally, the ASA pure-component density, pure-component vapor pressure, and solubility in various solvents in comparison to PC-SAFT predictions can be seen in Figures A1−A3 of the Supporting Information. Ethyl acetate and acetonitrile were considered as induced-associating compounds as proposed by Kleiner and Sadowski.44 Binary interaction parameters used and determined in this work are summarized in Table 4. Results of solubility calculations using these parameters are shown in Figures A4−A6 of the Supporting Information. The

Figure 6. (a) PXRD diffractogram of CBZ/SA CC obtained from slurry crystallization at screening compositions obtained from the SCA and (b) the reference PXRD diffractogram derived from SCXRD data (MOXWAY) taken from the Cambridge Structural Database.40

induces supersaturation and therewith crystallization via cooling. Aiming for screening point II at a certain (end) temperature (Figure 7), an unsaturated solution of that

Figure 7. Scheme of the cooling crystallization starting from a screening composition II determined using SCA or TA. The black line and gray line represent the solubility lines of the target (end) temperature and starting temperature, respectively. The CC regions at the end temperature and starting temperature are highlighted in dark gray and light gray, respectively.

composition is prepared at a higher temperature (start temperature in Figure 7). During cooling, the solubility of API, CF, and CC decreases, the solution becomes supersaturated, and thus crystallization occurs. Due to the different screening temperatures for slurry crystallization (298.15K) and cooling crystallization (288.15 K), the pure-component solubilities differ, and therefore, the same applies to the SCA-obtained screening compositions for the two screening methods. The screening compositions estimated at 288.15 K (the end temperature) are summarized in Table 2, and the one for the system CBZ/ASA/ethanol is

Table 2. Screening Compositions Obtained from the SCA at 288.15 K Using the Stated Lever Ratios as Well as the Resulting Crystalline Phases for Four Ternary Systems Obtained via Crystallization upon Cooling from 308.15 to 288.15 K API/CF

solvent

wAPI [g g−1]

wCF [g g−1]

lever ratio

crystals

CBZ/ASA

ethanol ethyl acetate acetonitrile methanol

0.041 0.019 0.058 0.081

0.160 0.088 0.078 0.184

0.98 0.95 0.99 0.96

CC CC + ASA CC + ASA CC

3258



Article

Table 3. PC-SAFT Pure-Component Parameters of the Compounds Investigated in This Work compound

Mi [g mol−1]

mseg [-]

σi [Å]

ui/kB [K]

εAiBi/kB [K]

κAiBi [-]

Niassoc

ref

CBZ ASA SA ethanol ethyl acetate acetonitrile methanol

236.27 180.16 138.12 46.07 88.11 41.05 32.04

9.9778 3.3000 7.8979 2.3827 3.5375 2.329 1.5255

2.6583 4.0992 2.6719 3.1771 3.3079 3.1898 3.23

151.55 416.81 238.72 198.24 230.8 311.31 188.9

1094.0 800.0 1972.6 2653.4 0 0 2899.5

0.02 0.03 0.0003 0.0324 0.01 0.01 0.0352

1/1 3/3 1/1 1/1 1/1 1/1 1/1

29 41 42 35 34 43 35

Table 4. PC-SAFT Binary Interaction Parameters, References for Parameters and for Experimental Data for Systems Investigated in This Work CBZ/ethanol CBZ/ethyl acetate CBZ/acetonitrile CBZ/methanol ASA/ethanol ASA/ethyl acetate ASA/acetonitrile ASA/methanol SA/ethanol SA/ethyl acetate SA/acetonitrile SA/methanol CBZ/ASA CBZ/SA

kij

temperature range [K]

a

278.80−338.16 298.15 298.15 276.8−326.8 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15

0.0791 0.0372 b

0.0228 −0.0131 0.023 0.0077 −0.0937 −0.0450 0.0225 −0.1328 0 −0.07

ref for parameters 29 29 this 29 this this this this this this this this this this

298.15

ref for experimental data 39 45 this 39 this this this this this this this this this this

work work work work work work work work work work work

work work work work work work work work work work work

kij = −1.48 × 10−4 × T[K] + 0.079. bkij = −1.22 × 10−4 × T[K] + 0.0321.

a

crystallizations using the screening compositions estimated via the TA. Pure CCs of CBZ/ASA were found in screening experiments at all screening compositions obtained from the TA. An example diffractogram of the CC is shown in Figure 5. The application of the TA for the system CBZ/SA yielded in the formation of a mixture of CC and SA crystals in the three solvents ethanol, ethyl acetate, and methanol, whereas pure CCs of CBZ/SA were found in acetonitrile (see diffractogram in Figure 6). Comparing TA and SCA, it becomes obvious that both approaches lead to appropriate results for screening compositions suitable for CC generation via slurry crystallization. CCs were found for all screening compositions determined by either SCA or TA. In some cases, mixtures of CCs and CF crystals were found for both, SCA and TA. Thus, the SCA provides as good results for the screening composition as the TA with a considerably lower modeling effort.

melting properties required for solubility calculations (eq 1) are summarized in Table 5. Table 5. Melting Properties of the APIs and CFs Utilized in This Work compound

TSL 0i [K]

−1 ΔhSL 0i [kJ mol ]

SL ΔcP,0i [J mol−1 K−1]

ref

CBZ (III) ASA SA

447.95 408.15 431.35

26.82 25.60 27.09

65.17 0 60.70

46, 47 48 49

4.2.2. Slurry Crystallization for Co-crystal Screening (TA). The TA-obtained screening compositions of the prepared slurries and the resulting crystalline phases can be found in Table 6. The screening composition of the system CBZ/ASA/ ethanol is illustrated in Figure 4a as a black star, which is located in the CC region highlighted in gray, and consequently, pure CCs were formed in ethanol during the screening experiment. CC formation was indeed observed for all slurry

Table 6. Screening Compositions Obtained from the TA Using the Stated Lever Ratio as Well as the Resulting Crystalline Phases Obtained from Slurry Crystallization at These Screening Points for Eight Ternary Systems at 298.15 K API/CF

solvent

wAPI [g g−1]

wCF [g g−1]

lever ratio

crystals

CBZ/ASA

ethanol ethyl acetate acetonitrile methanol ethanol ethyl acetate acetonitrile methanol

0.163 0.188 0.188 0.163 0.148 0.171 0.214 0.124

0.261 0.185 0.190 0.324 0.330 0.250 0.176 0.368

0.8 0.7 0.8 1.15 0.8 0.78 0.78 0.85

CC CC CC CC CC + SA CC + SA CC CC + SA

CBZ/SA

3259



Article

Table 7. Screening Compositions Obtained from the TA at 288.15 K Using the Stated Lever Ratio as Well as the Resulting Crystalline Phases Obtained from Cooling Crystallization from 308.15 to 288.15 K for Four Ternary Systems API/CF

solvent

wAPI [g g−1]

wCF [g g−1]

lever ratio

crystals

CBZ/ASA

ethanol ethyl acetate acetonitrile methanol

0.038 0.034 0.059 0.143

0.165 0.080 0.079 0.325

1 1 1 1

CC CC + ASA CC + ASA CC + ASA

Figure 8. Mass-fraction solubilities of (a) CBZ, ASA, and their CC in ethanol and (b) CBZ, SA, and their CC in ethanol at 298.15 K (shortened axis). The experimental solubility of CBZ is depicted by gray squares, the solubility of the CF is depicted by gray circles (a) ASA and (b) SA, measured eutectic points are shown as gray triangles, and pure CC solubilities are depicted by gray stars. The black star represents the fitting point for the CC solubility product, and the solid lines are the PC-SAFT modeled solubilities.

and SA. This binary interaction parameter was fitted to the experimentally determined solubility of CBZ in the presence of SA (ternary system CBZ/SA/ethanol). The solubility products of the CCs (eq 3) were determined by fitting to one experimentally determined solubility of the CCs in ethanol (black stars in Figure 8) and subsequently used to predict the solubility lines of the CCs in ethanol but also in other solvents (see section 4.4). The solubility products Ks,CC are 7.87 × 10−4 and 3.49 × 10−4 for the systems CBZ/ASA and CBZ/SA, respectively. As can be seen from Figure 8, the PC-SAFTpredicted phase behavior and particularly the width and shape of the CC region differ considerably for the CBZ/ASA and CBZ/SA systems, although the molecular structure of ASA and SA is quite similar. This is in surprisingly good agreement with the experimentally determined solubilities. 4.4. Selection of Best-Suited Solvents for CC Generation. The TA is now used to determine the bestsuited solvent for CC generation. For that purpose, several criteria have to be considered: (I) the solvent has to be volatile to evaporate completely from the CC after production; (II) the solvent needs to be regarded as safe by the ICH guidelines;50 (III) solvate formation of the solvent with either the API or CF should be avoided to keep the system as simple as possible; (IV) the CC region has to be as wide as possible to increase the yield of the production process.21 The latter criterion can only be evaluated using the ternary phase diagram in the API/CF/solvent system, which can be determined as described in section 3.4 and is depicted as an example in Figure 8. Generating such a phase diagram usually requires a huge experimental effort. However, using the TA, the experimental effort can be reduced to a minimum, since only one API/CF/solvent system must be determined experimentally to obtain the (solvent-independent) solubility product (eq 3). Once determined, this solubility product can be applied to predict the solubility of the CC in any other solvent or even solvent mixture.27 This only additionally

4.2.3. Cooling Crystallization for Co-crystal Screening (TA). Finally, the TA was used to generate screening compositions for the CBZ/ASA CC formation via cooling crystallization. The obtained screening compositions in the four ternary systems can be seen in Table 7. As an example, the screening composition for the system CBZ/ASA/ethanol is illustrated as a black star in Figure 4b. As the composition is located in the gray area, consequently, pure CCs crystallized at the end temperature of 288.15 K. A mixture of CCs and ASA crystals formed in the solvents ethyl acetate, acetonitrile, and methanol. Similarly to the findings in section 4.1.2, the slurry crystallization seems to be advantageous compared to the cooling crystallization for finding pure CCs from solutions of TA-defined screening compositions. Analogous to the comparison of SCA and TA for the slurry crystallization, it becomes obvious that both approaches generate reasonable screening compositions for the cooling crystallization. CCs were found for all screening compositions determined by either SCA or TA, whereas mixtures of CCs and CF crystals were found for both, SCA and TA, for some systems. Thus, using the SCA and TA considerably lowers the experimental effort for CC screening. Furthermore, the SCA can be used just based on the pure-component solubilities of API and CF without additional modeling effort. 4.3. Modeling of CC Phase Diagrams (TA). In contrast to SCA, the TA not only can be used to generate suitable screening compositions for CC screening but also is able to model and to predict phase diagrams of CC systems. Parts (a) and (b) in Figure 8 show the PC-SAFT modeling for the systems CBZ/ASA/ethanol and CBZ/SA/ethanol, respectively. PC-SAFT was used to model the solubilities of CBZ, ASA, and SA in the three-component mixtures CBZ/ASA (SA)/ethanol according to eq 1, whereas the solubility of the CCs was modeled using eq 3. The modeling of the system CBZ/SA has been performed using an additional binary interaction parameter between CBZ 3260



Article

Figure 9. Ternary phase diagrams of CBZ/ASA and the solvents (a) ethanol, (b) ethyl acetate, (c) acetonitrile, and (d) methanol at 298.15 K. The black lines are the phase boundaries predicted by PC-SAFT with the predicted CC region highlighted in gray. The gray squares represent eutectic points obtained from measurements in this work.

best solvent for the production of CBZ/SA CCs, determined from the TA. The comparison of experimentally determined phase diagrams with PC-SAFT predictions for this system can be seen in Figure A7 of the Supporting Information. The above-shown TA predictions were carried out for isothermal conditions, e.g., for slurry crystallization. For CC production via cooling crystallization, varying temperatures and therefore shifting solubility lines have to be considered. Determining the ternary phase diagrams at different temperatures would require a quite intensive experimental effort. The potential of using PC-SAFT to predict phase diagrams at different temperatures was already shown by Lange and Sadowski.29 It thus also allows for predicting the solubility shift as a function of temperature and thus estimating the CC production capabilities via cooling crystallization based on very few experiments only.

requires the pure-component solubilities of API and CF in these solvents to predict the complete phase diagram. The purpose of the TA is the qualitative accordance with the experimental phase diagram in order to evaluate the suitability of the solvent, rather than quantitative agreement with experimentally determined solubility data. The phase diagram of CBZ/ASA in ethanol (Figure 9a) was used to determine the solubility product which was used afterward to predict the phase diagrams of CBZ/ASA in ethyl acetate, acetonitrile, and methanol (Figure 9b−d). The predicted eutectic points, which characterize the width and the shift of the CC region, agree surprisingly well with the experimentally determined eutectic points shown in Figure 9. Thus, the PC-SAFT prediction can evaluate the width of the CC region with similar quality as time-consuming experiments and therewith can drastically reduce the experimental efforts. Figure 9 also indicates that the phase behavior of CC systems strongly depends on the solvent. The width as well as the shift of the CC region significantly differs for the considered solvents. It can be seen that CBZ, ASA, and their CC have the highest solubility in methanol. The ASA solubility in the other solvents is 3−6 times higher than the solubility of CBZ. CBZ and ASA are almost congruently soluble in acetonitrile. All solvents are sufficiently volatile (criterion I) and do not form solvates with the investigated solutes (III). Thus, the criteria II and IV are decisive for the selection of the best solvent. Ethanol leads to a sufficiently big CC region and has a lower toxicity compared to methanol (II), which would lead to an even bigger CC region. Ethyl acetate and acetonitrile result in a very narrow CC region which would lead to a lower yield for CC production (IV). Therefore, among the investigated solvents, ethanol seems to be the best-suited solvent for the production of CBZ/ASA. Ethanol also turned out to be the

5. CONCLUSION In this work, we proposed two approaches, namely, a shortcut approach (SCA) and a thermodynamic approach (TA) to obtain screening compositions best-suitable for the experimental co-crystal (CC) screening. The SCA assumes that the solubility of one of the two CC components in a common solvent is not influenced by the presence of the other one. It is a reliable and very simple approach since only the purecomponent solubilities of API (here CBZ) and coformer CF (here SA or ASA) in each solvent as well as the stoichiometry of the expected CC have to be known. In the case that the stoichiometry is unknown prior to the screening, only one screening composition has to be prepared for each stoichiometry to screen for. The TA uses the thermodynamic model PC-SAFT to encounter for thermodynamic nonidealities in the API/CF/ solvent system when estimating suitable screening composi3261



Article

tions for CC generation. An important additional feature of the two developed approaches is the possibility to adjust the amount of crystals present in the slurry or at the end of cooling to ensure enough CC material for crystal characterization. On the basis of the screening compositions estimated via SCA or TA, CC screening was performed using slurry crystallization and cooling crystallization. The CC screening using slurry crystallization was performed for carbamazepine (CBZ) with the coformers (CFs) acetylsalicylic acid (ASA) and salicylic acid (SA) in the solvents ethanol, ethyl acetate, acetonitrile, and methanol, whereas cooling crystallization was performed for CCs of CBZ and ASA in the before-mentioned solvents. The formation of CCs could be verified for all systems using both, slurry and cooling crystallization, with screening compositions obtained from either of the two approaches, meaning that suitable compositions for experimental CC screening were generated using the SCA or the TA. The use of screening compositions obtained from both approaches significantly increases the probability of successful CC screening compared to state-of-the-art approaches, while, at the same time, it considerably reduces the experimental effort. In contrast to the SCA, the TA can also be used to select the best-suited solvent for CC production with minimum additional effort via predicting the phase diagram of the CC system in various solvents. Currently, this information has to be generated experimentally for a huge number of solvents/ compositions in order to select the best-suited solvent for CC generation. The use of the TA enables minimizing this high experimental effort, as only one phase diagram of API/CF/ solvent has to be determined experimentally, and this information is then used to predict the phase diagrams in any other solvents. A very good agreement of the TA-predicted phase diagrams in the ternary systems with the experimentally determined ones was found for CC systems of CBZ with both, ASA and SA, in the solvents ethanol, ethyl acetate, acetonitrile, and methanol. As a result, ethanol turned out to be the bestsuited solvent among these for the production of the CBZ/ ASA and CBZ/SA CCs. The TA thus enables generating suitable screening compositions for experimental CC screening and can furthermore be used to determine phase diagrams to select the best-suited solvents for CC production with minimum experimental effort.

■

Miko Schleinitz: 0000-0003-4995-5679 Gabriele Sadowski: 0000-0002-5038-9152 Notes

The authors declare no competing financial interest.

■ ■

ACKNOWLEDGMENTS The authors thank Johanna Topphoff for measurements on cocrystal screening using cooling crystallization.

Notation

a,molar Helmholtz energy [J mol−1] ΔcSL P,0i,difference of the heat capacity of the solid and the liquid component i at its melting point [kJ K−1 kg−1] −1 ΔhSL 0i ,heat of fusion of component i [kJ kg ] kij,binary interaction parameter [-] Ks,CC,co-crystal solubility product [-] miseg,number of segments of component i [-] R,gas constant [J mol−1 K−1] T,temperature [K] TSL 0i ,melting temperature of component i [K] ui/kB,dispersion energy parameter [K] wi,mass fraction of component i [-] xi,mole fraction of component i [-]

Abbreviations

API,active pharmaceutical ingredient ASA,acetylsalicylic acid CBZ,carbamazepine CC,co-crystal CF,coformer ICH,International Council for Harmonisation L,liquid phase PC-SAFT,perturbed-chain statistical associating fluid theory PXRD,Powder X-ray diffraction SA,salicylic acid SCA,short-cut approach TA,thermodynamic approach Greek Symbols

γi, activity coefficient of component i [-] εAiBi/kB, association energy parameter [K] κAiBi, association volume parameter [-] νi, stoichiometric coefficient of component i [-] σi, segment diameter [Å]

Subscripts

ASSOCIATED CONTENT

i,j,component i, component j

■

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.cgd.9b00103. PC-SAFT pure-component parameter determination of aspirin; comparison of modeled solubility data with solubility data measured in this work and available from the literature; ternary phase diagram of carbamazepine/ salicylic acid in ethanol, ethyl acetate, acetonitrile, and methanol (PDF)

■

NOMENCLATURE

REFERENCES

(1) McNamee, L. M.; Walsh, M. J.; Ledley, F. D. Timelines of translational science: From technology initiation to FDA approval. PLoS One 2017, 12 (5), e0177371. (2) Jones, W.; Motherwell, W. S.; Trask, A. V. Pharmaceutical Cocrystals: An Emerging Approach to Physical Property Enhancement. MRS Bull. 2006, 31 (11), 875−879. (3) Babu, N. J.; Nangia, A. Solubility Advantage of Amorphous Drugs and Pharmaceutical Cocrystals. Cryst. Growth Des. 2011, 11 (7), 2662−2679. (4) Nangia, A. K.; Desiraju, G. R. Crystal Engineering. An Outlook for the Future. Angew. Chem., Int. Ed. 2019, 58, 4100. (5) Aitipamula, S.; Banerjee, R.; Bansal, A. K.; Biradha, K.; Cheney, M. L.; Choudhury, A. R.; Desiraju, G. R.; Dikundwar, A. G.; Dubey, R.; Duggirala, N.; Ghogale, P. P.; Ghosh, S.; Goswami, P. K.; Goud, N. R.; Jetti, R. R. K. R.; Karpinski, P.; Kaushik, P.; Kumar, D.; Kumar, V.; Moulton, B.; Mukherjee, A.; Mukherjee, G.; Myerson, A. S.; Puri,

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +49 (0) 231 755 2635. Fax: +49 (0)231 755 2572. ORCID

Heiner Veith: 0000-0003-4526-4547 3262



Article

V.; Ramanan, A.; Rajamannar, T.; Reddy, C. M.; Rodriguez-Hornedo, N.; Rogers, R. D.; Row, T. N. G.; Sanphui, P.; Shan, N.; Shete, G.; Singh, A.; Sun, C. C.; Swift, J. A.; Thaimattam, R.; Thakur, T. S.; Kumar Thaper, R.; Thomas, S. P.; Tothadi, S.; Vangala, V. R.; Variankaval, N.; Vishweshwar, P.; Weyna, D. R.; Zaworotko, M. J. Polymorphs, Salts, and Cocrystals: What’s in a Name? Cryst. Growth Des. 2012, 12 (5), 2147−2152. (6) Almarsson, Ö .; Zaworotko, M. J. Crystal engineering of the composition of pharmaceutical phases. Do pharmaceutical co-crystals represent a new path to improved medicines? Chem. Commun. 2004, 17, 1889−1896. (7) Fábián, L. Cambridge Structural Database Analysis of Molecular Complementarity in Cocrystals. Cryst. Growth Des. 2009, 9 (3), 1436−1443. (8) Delori, A.; Galek, P. T. A.; Pidcock, E.; Patni, M.; Jones, W. Knowledge-based hydrogen bond prediction and the synthesis of salts and cocrystals of the anti-malarial drug pyrimethamine with various drug and GRAS molecules. CrystEngComm 2013, 15 (15), 2916. (9) Bhogala, B. R.; Basavoju, S.; Nangia, A. Tape and layer structures in cocrystals of some di- and tricarboxylic acids with 4,4′-bipyridines and isonicotinamide. From binary to ternary cocrystals. CrystEngComm 2005, 7, 551−562. (10) Mohammad, M. A.; Alhalaweh, A.; Velaga, S. P. Hansen solubility parameter as a tool to predict cocrystal formation. Int. J. Pharm. 2011, 407 (1), 63−71. (11) Abramov, Y. A. Current Computational Approaches to Support Pharmaceutical Solid Form Selection. Org. Process Res. Dev. 2013, 17 (3), 472−485. (12) He, G.; Chow, P. S.; Tan, R. B. H. Predicting Multicomponent Crystal Formation: The Interplay between Homomeric and Heteromeric Interactions. Cryst. Growth Des. 2009, 9 (10), 4529− 4532. (13) Grecu, T.; Adams, H.; Hunter, C. A.; McCabe, J. F.; Portell, A.; Prohens, R. Virtual Screening Identifies New Cocrystals of Nalidixic Acid. Cryst. Growth Des. 2014, 14 (4), 1749−1755. (14) Hoxha, K.; Case, D. H.; Day, G. M.; Prior, T. J. Cocrystallisation of cytosine with 1, 10-phenanthroline: computational screening and experimental realisation. CrystEngComm 2015, 17 (37), 7130−7141. (15) Malamatari, M.; Ross, S. A.; Douroumis, D.; Velaga, S. P. Experimental cocrystal screening and solution based scale-up cocrystallization methods. Adv. Drug Delivery Rev. 2017, 117, 162− 177. (16) Sheikh, A. Y.; Rahim, S. A.; Hammond, R. B.; Roberts, K. J. Scalable solution cocrystallization: Case of carbamazepine-nicotinamide I. CrystEngComm 2009, 11 (3), 501−509. (17) Aitipamula, S.; Chow, P. S.; Tan, R. B. H. Structural, Spectroscopic and Thermal Analysis of Cocrystals of Carbamazepine and Piracetam with Hydroquinone. J. Chem. Crystallogr. 2011, 41 (11), 1604−1611. (18) Qiao, N.; Li, M.; Schlindwein, W.; Malek, N.; Davies, A.; Trappitt, G. Pharmaceutical cocrystals: an overview. Int. J. Pharm. 2011, 419 (1−2), 1−11. (19) Childs, S. L.; Rodríguez-Hornedo, N.; Reddy, L. S.; Jayasankar, A.; Maheshwari, C.; McCausland, L.; Shipplett, R.; Stahly, B. C. Screening strategies based on solubility and solution composition generate pharmaceutically acceptable cocrystals of carbamazepine. CrystEngComm 2008, 10 (7), 856. (20) Rodríguez-Hornedo, N.; Nehm, S. J.; Seefeldt, K. F.; PaganTorres, Y.; Falkiewicz, C. J. Reaction crystallization of pharmaceutical molecular complexes. Mol. Pharmaceutics 2006, 3 (3), 362−367. (21) Rager, T.; Hilfiker, R. Application of Phase Diagrams in Cocrystal Search and Preparation. In Pharmaceutical Salts and Co-crystals; Wouters, J., Quéré, L., Eds.; Royal Society of Chemistry: Cambridge, U.K., 2011; Chapter 12, pp 280−299. (22) Hong, C.; Xie, Y.; Yao, Y.; Li, G.; Yuan, X.; Shen, H. A novel strategy for pharmaceutical cocrystal generation without knowledge of stoichiometric ratio: myricetin cocrystals and a ternary phase diagram. Pharm. Res. 2015, 32 (1), 47−60.

(23) Leung, D. H.; Lohani, S.; Ball, R. G.; Canfield, N.; Wang, Y.; Rhodes, T.; Bak, A. Two Novel Pharmaceutical Cocrystals of a Development Compound - Screening, Scale-up, and Characterization. Cryst. Growth Des. 2012, 12 (3), 1254−1262. (24) Bhatt, P. M.; Azim, Y.; Thakur, T. S.; Desiraju, G. R. Cocrystals of the anti-HIV drugs lamivudine and zidovudine. Cryst. Growth Des. 2009, 9 (2), 951−957. (25) Rager, T.; Hilfiker, R. Cocrystal Formation from Solvent Mixtures. Cryst. Growth Des. 2010, 10 (7), 3237−3241. (26) Chiarella, R. A.; Davey, R. J.; Peterson, M. L. Making CoCrystalsThe Utility of Ternary Phase Diagrams. Cryst. Growth Des. 2007, 7 (7), 1223−1226. (27) Lange, L.; Heisel, S.; Sadowski, G. Predicting the Solubility of Pharmaceutical Cocrystals in Solvent/Anti-Solvent Mixtures. Molecules 2016, 21 (5), 593. (28) Lange, L.; Lehmkemper, K.; Sadowski, G. Predicting the Aqueous Solubility of Pharmaceutical Cocrystals As a Function of pH and Temperature. Cryst. Growth Des. 2016, 16 (5), 2726−2740. (29) Lange, L.; Sadowski, G. Thermodynamic Modeling for Efficient Cocrystal Formation. Cryst. Growth Des. 2015, 15 (9), 4406−4416. (30) Lange, L.; Sadowski, G. Polymorphs, Hydrates, Cocrystals, and Cocrystal Hydrates: Thermodynamic Modeling of Theophylline Systems. Cryst. Growth Des. 2016, 16 (8), 4439−4449. (31) Lange, L.; Schleinitz, M.; Sadowski, G. Predicting the Effect of pH on Stability and Solubility of Polymorphs, Hydrates, and Cocrystals. Cryst. Growth Des. 2016, 16 (7), 4136−4147. (32) Zhang, G. G. Z.; Henry, R. F.; Borchardt, T. B.; Lou, X. Efficient co-crystal screening using solution-mediated phase transformation. J. Pharm. Sci. 2007, 96 (5), 990−995. (33) Prausnitz, J. M.; Lichtenthaler, R. N.; de Azevedo, E. G. Molecular thermodynamics of fluid-phase equilibria, 3rd ed.; Prentice Hall PTR: Upper Saddle River, NJ, 1998. (34) Gross, J.; Sadowski, G. Perturbed-Chain SAFT: An Equation of State Based on a Perturbation Theory for Chain Molecules. Ind. Eng. Chem. Res. 2001, 40 (4), 1244−1260. (35) Gross, J.; Sadowski, G. Application of the Perturbed-Chain SAFT Equation of State to Associating Systems. Ind. Eng. Chem. Res. 2002, 41 (22), 5510−5515. (36) Wolbach, J. P.; Sandler, S. I. Using molecular orbital calculations to describe the phase behavior of cross-associating mixtures. Ind. Eng. Chem. Res. 1998, 37 (8), 2917−2928. (37) Almarsson, O.; Hickey, M. B.; Peterson, M. L.; Zaworotko, M. J.; Moulton, B.; Rodríguez-Hornedo, N. Pharmaceutical Co-Crystal Compositions of Drugs such as Carbamazepine, Celecobix, Olantapine, Itraconazole, Topiramate, Modafinil, 5-Fluorouracil, Hydrochlorothiazide, Acetaminophen, Aspirin, Flurbiprofen, Phenytoin and Ibuprofen. U.S. Patent 2007/0059356 A1, 2007. (38) Vishweshwar, P.; McMahon, J. A.; Oliveira, M.; Peterson, M. L.; Zaworotko, M. J. The predictably elusive form II of aspirin. J. Am. Chem. Soc. 2005, 127 (48), 16802−16803. (39) Liu, W.; Dang, L.; Black, S.; Wei, H. Solubility of Carbamazepine (Form III) in Different Solvents from (275 to 343) K. J. Chem. Eng. Data 2008, 53 (9), 2204−2206. (40) Allen, F. H. The Cambridge Structural Database: A quarter of a million crystal structures and rising. Acta Crystallogr., Sect. B: Struct. Sci. 2002, 58 (3), 380−388. (41) Pototzki, C. Personal communication. TU Dortmund, Dortmund, Germany, 2017. (42) Reschke, T.; Zherikova, K. V.; Verevkin, S. P.; Held, C. Benzoic Acid and Chlorobenzoic Acids: Thermodynamic Study of the Pure Compounds and Binary Mixtures With Water. J. Pharm. Sci. 2016, 105 (3), 1050−1058. (43) Kleiner, M.; Gross, J. An equation of state contribution for polar components: Polarizable dipoles. AIChE J. 2006, 52 (5), 1951− 1961. (44) Kleiner, M.; Sadowski, G. Modeling of Polar Systems Using PCP-SAFT: An Approach to Account for Induced-Association Interactions. J. Phys. Chem. C 2007, 111 (43), 15544−15553. 3263



Article

(45) Nehm, S. J.; Rodríguez-Spong, B.; Rodríguez-Hornedo, N. Phase Solubility Diagrams of Cocrystals Are Explained by Solubility Product and Solution Complexation. Cryst. Growth Des. 2006, 6 (2), 592−600. (46) Behme, R. J.; Brooke, D. Heat of fusion measurement of a low melting polymorph of carbamazepine that undergoes multiple-phase changes during differential scanning calorimetry analysis. J. Pharm. Sci. 1991, 80 (10), 986−990. (47) Grzesiak, A. L.; Lang, M.; Kim, K.; Matzger, A. J. Comparison of the Four Anhydrous Polymorphs of Carbamazepine and the Crystal Structure of Form I. J. Pharm. Sci. 2003, 92 (11), 2260−2271. (48) Abildskov, J. Solubility and Related Properties of Large Complex Chemicals: Part 2; DECHEMA Chemistry Data Series; DECHEMA: Frankfurt am Main, Germany, 2005. (49) Nordström, F. L.; Rasmuson, Å. C. Determination of the activity of a molecular solute in saturated solution. J. Chem. Thermodyn. 2008, 40 (12), 1684−1692. (50) ICH. Impurities: Guideline for Residual Solvents Q3C(R6), Step 4th version; ICH: Geneva, Switzerland, 2016; p 34.

3264


Thermodynamic Approach for Co-crystal Screening | Crystal Growth

Recommend Documents