Taxonomy of Cocrystal Ternary Phase Diagrams - Journal of Chemical

Article pubs.acs.org/jced

Taxonomy of Cocrystal Ternary Phase Diagrams Richard B. McClurg* SSCI, a Division of Albany Molecular Research Inc. (AMRI), West Lafayette, Indiana 47906, United States S Supporting Information *

ABSTRACT: A taxonomy of cocrystal ternary phase diagrams is presented. It is based upon an enumeration of distinct ternary phase diagrams as functions of the free energy of formation for each of a selected set of crystalline phases. In addition to topologically distinct diagrams, phase diagrams are distinguished as to the congruent or incongruent dissolution of the cocrystalline phase. The diagrams are organized according to the set of solid phases and the number of three-phase regions. Phase diagrams and free energy surfaces are provided for representative examples of each illustrated case.

1. INTRODUCTION Multicomponent solids are commonly used in the pharmaceutical industry to deliver active pharmaceutical ingredients (APIs). Solids are desirable to confer physical and chemical stability with the convenience of solid oral dosage (tablets). For many APIs there are several solid forms available, and one must be chosen for development. Options include salts,1 hydrates,2 solvates,3 and cocrystals.4 For the present purposes, a cocrystal is defined as a crystalline phase that contains an API and another molecular species other than water or solvent, called the coformer. It is assumed that both the pure API and coformer are solids and that the solvent is a liquid at the temperature and pressure of interest. The most common processes for producing cocrystals are solvent-based. Three-component phase diagrams (API, coformer, and solvent) are beginning to be used to understand cocrystal systems.5−8 Phase-coexistence loci have typically been fit using algebraic expressions derived from idealized equilibrium models.7 Here the connection between the free energy surface and the phase diagram is used to develop a taxonomy of cocrystal phase diagrams. Typical phase diagrams present either the thermodynamic equilibrium properties of a pure substance as a function of thermodynamic state variables (e.g., water phases as a function of temperature and pressure) or of mixtures as a function of composition and thermodynamic state variables (e.g., water/ ethanol phases as a function of temperature at fixed pressure). For these diagrams the intent is to accurately portray the thermodynamic behavior of real systems. Global phase diagrams are qualitatively different in that they present the phase behavior of a continuum of systems as a function of model parameters. The classification system for binary phase diagrams based on the van der Waals equation of state developed by P. H. van Konynenburg and R. L. Scott is an early example of a global phase diagram.9 In that analysis, the system parameters determine the topology of the critical locus of a binary mixture. Alternatively, global phase diagrams have © XXXX American Chemical Society

been constructed as a function of parameters in a generic intermolecular potential. This approach has been used to explore crystal structures as functions of intermolecular potential parameters,10−13 for instance. In either case, global phase diagrams are useful for constructing classification systems since they present the possible behaviors consistent with the generic model. Since the intent of global phase diagrams is to enumerate possibilities rather than to accurately represent a particular system, global phase diagrams are typically based upon simplified models with a limited parameter set. It is difficult to apply global phase diagrams to multicomponent systems containing both fluid and solid phases. Each solid phase has its own free energy surface separate from that of the fluid phases. Therefore, global phase diagrams based on generalized equations of state are not applicable to systems containing both fluid and solids. On the other hand, the use of a generic intermolecular potential is complicated by the need for accurate potentials describing the interactions of each of the pairs of components in each of the phases. In order to generate a taxonomy of ternary phase diagrams for cocrystal systems, a simplified model is needed that is rich enough to represent a wide variety of behaviors without too large a parameter set to explore exhaustively.

2. COMPUTATIONAL METHODS In order to generate a suitable thermodynamic model, a number of simplifying assumptions are invoked. Each phase diagram presents isothermal and isobaric equilibrium phase behavior as a function of the mole fractions for three components: a solvent (denoted as S), an active pharmaceutical ingredient (denoted as A), and a coformer (denoted as C). The Special Issue: Proceedings of PPEPPD 2016 Received: September 7, 2016 Accepted: November 9, 2016

A

DOI: 10.1021/acs.jced.6b00791 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Figure 1. Example free energy surfaces and projections onto ternary phase diagrams depicting (a) the fluid-phase free energy surface (yellow), (b) the crystalline API (red dot) and two-phase coexistence surface (green), (c) the crystalline coformer and two-phase coexistence surface, (d) the cocrystal and two-phase coexistence surface, (e) the solvated cocrystal and two-phase coexistence surface, and (f) the eutectic (purple dot) and three-phase coexistence region (blue).

and solvent) crystalline phase is present as a stable phase in each diagram. The number of solid phases is selected to form a class of phase diagrams. Within each class, the stoichiometry of each solid phase is fixed and the free energies of formation relative to the pure components are varied to generate representative diagrams. The diagrams are arranged in rows according to the number of three-phase regions. Congruent and incongruent cocrystals are distinguished. Otherwise, only examples of topologically distinct diagrams are included in the taxonomy. Constitutive Constructions. Constituent constructions necessary to produce cocrystal ternary phase diagrams from free energy surfaces are illustrated in Figure 1. Figure 1a shows the free energy surface for the solution phase, assumed to be an

temperature domain is restricted to lie between the melting and boiling points of the solvent and below the melting points of both the API and the coformer. This ensures that the liquid solvent and crystalline API and coformer phases appear at the vertices of each of the phase diagrams. Ideal liquid mixtures are assumed, so fluid−fluid phase separation is not considered. No chemical reactions among the components are considered, so each molecular species is an independent component. The free energy reference state for each component is the pure fluid at the temperature and pressure of interest. Only stoichiometric crystalline phases (no variable solvates) are considered. Therefore, the composition of each of the crystalline phases is fixed. At least one cocrystal (containing the API and coformer) or solvated cocrystal (containing the API, coformer, B



Article

Figure 1e illustrates the free energy surface and saturated solutions for a solvated cocrystal, again using the same color scheme. The illustration is for a 1:1:1 stoichiometry for simplicity, but other stoichiometries are also possible. Since the derivative of the solution free energy surface diverges at the boundaries, the saturated solution locus for a solvated cocrystal is a closed loop for any stoichiometry and any negative value of the free energy of fusion. Recall that the free energy of fusion is the difference between the free energy of formation (Gf) and the free energy of mixing of its components (Gmix). Figure 1f illustrates the free energy surfaces and saturated solutions for a crystalline API and a cocrystal. As drawn, there is a single solution composition, denoted with a purple dot, that is in equilibrium with both crystalline phases. This is a eutectic. The crystalline-phase free energies and eutectic free energy constitute the corners of a triangular region. Within this region, the system free energy is minimized by splitting of the system into the three phases whose compositions are given by the vertices of the triangle. The three-phase regions are shown as blue triangles on both the free energy surface and the ternary phase diagram. If the free energies of formation of three solid phases are sufficiently negative, then a three-phase region defined by the three solids appears in the phase diagram. This possibility is not illustrated in Figure 1 but is discussed in the context of solvated cocrystals. Free Energy Surfaces and Ternary Phase Diagrams. In order to construct a taxonomy of cocrystal ternary phase diagrams, consider the solution free energy surface shown in Figure 1a and select a list of solid phases for inclusion. For the diagram to represent a cocrystal system, the list should include the API and coformer and at least one solid phase containing both the API and coformer. Assign a small negative free energy of fusion (Gf − Gmix) to each solid phase such that the binary phase-coexistence regions for each of the solid phases do not intersect. This corresponds to a condition in which each of the solids is close to its melting or dissolution temperature. It yields the simplest phase diagram consistent with the assumed list of solid phases. Next, consider cases in which the free energies of fusion are larger in magnitude such that various pairs of solid phases are in equilibrium with a eutectic solution. Continue to consider cases in which multiple eutectics occur and the cocrystal remains on the minimum free energy surface. Enumeration of the topologically distinguishable cases yields a taxonomy of cocrystal ternary phase diagrams for the selected list of solid phases. The process is then repeated for a new list of solid phases. Since there are multiple choices for crystalline phases, the process is combinatorial, and the number of phase diagrams grows rapidly with the maximum number of crystalline phases included in the taxonomy. An example of a set of minimal free energy surfaces and their projection onto a basal plane to produce the ternary phase diagram is illustrated in Figure 2. Only surfaces corresponding to minimal free energies are shown. Continuations of the free energy surfaces to metastable states are not shown for clarity. The illustrated example corresponds to Figure 3d. Free energy surfaces for all of the ternary phase diagrams contained in Figures 3, 4, and 5 are provided in the Supporting Information. Animations illustrating the diagrams as viewed from different viewpoints are also provided to aid in visualization of the surfaces.

ideal mixture for simplicity. For an ideal mixture, the free energy of the solution is due to the entropy of mixing: G = kT

∑ xi ln(xi) i

(1)

Accurate fitting of experimental data generally requires a nonideal mixing model with additional parameters using a suitable excess free energy expansion.14−16 Although nonidealities are needed to fit experimental data for particular systems, the ideal-mixture free energy surface is sufficient to illustrate equilibrium between solids and solutions. Since there is only a single phase for all of the compositions in Figure 1a, the ternary phase diagram on the basal plane of the free energy diagram is featureless. Figure 1b−f depict two-phase coexistence surfaces in green. In each case a few representative tie lines are drawn between the crystal composition and the locus of saturated solutions, whose composition is given by ⎡ Gf ⎤ exp⎢ ⎥ = xAs xCt xSu ⎣ kT ⎦

(2)

where Gf is the molar free energy of formation of the crystal relative to its pure components, {xA, xC, xS} is the set of component mole fractions in the saturated solution, and {s, t, u} is the set of component mole fractions in the crystal. Equation 2 may be derived by determining the locus of points on the mixture free energy surface such that the normal vector (calculated using the surface gradient) is perpendicular to the tie lines to the crystal composition and free energy. A brief derivation of eq 2 is provided in the Supporting Information. Panels (b) and (c) of Figure 1 are for crystals of the pure API and coformer, respectively. Figure 1b illustrates equilibrium between the crystalline API and saturated solutions. The free energy of the crystalline API is represented by a red dot in the free energy space, and its composition is projected onto the ternary phase diagram. Since the red dot appears below the solution free energy surface at the same composition, the free energy of fusion (Gf − Gmix) is negative and the crystalline phase is stable. For compositions rich in API, the free energy of the system is minimized by splitting of the system into a crystalline API phase (s = 1, t = u = 0) and a solution phase depleted in the API (xA = exp[Gf/kT]). The composition of the solution phase is determined by the common tangent construction or, equivalently, by eq 2, and the amount of each phase by the lever rule. Illustrative tie lines are drawn as lines within the green-shaded two-phase region. The locus of saturated solutions and tie lines are also projected onto the ternary phase diagram shown on the basal plane of the free energy diagram. Figure 1c is analogous to Figure 1b, with the role of the API replaced by that of the coformer (t = 1, s = u = 0, xC = exp[Gf/kT]). Figure 1d illustrates equilibrium between a crystalline cocrystal and saturated solutions using the same color scheme as in the previous panels. For an unsolvated cocrystal, s + t = 1 and u = 0 in eq 2. The illustration is for a cocrystal with 1:1 stoichiometry (s = t = 1/2), but other stoichiometries are also possible. The phase equilibria for API and coformer solvates and their associated saturated solutions are drawn similarly to those of the cocrystals and are not shown in Figure 1 for brevity. For an API solvate, s + u = 1 and t = 0 in eq 2. Similarly, for a coformer solvate, t + u = 1 and s = 0 in eq 2. C



Article

complicated process utilizing an excess of one of the components or identification of another solvent in which the cocrystal is congruent. Panels (d) and (e) of Figure 3 similarly form a topologically equivalent pair of diagrams distinguished on the basis of the congruency of the cocrystal in Figure 3d and the incongruent cocrystal in Figure 3e. Likewise, Figure 3g illustrates a congruent cocrystal, while Figure 3f,h illustrate incongruent cases. Many of the reported cocrystal ternary phase diagrams contain one unsolvated cocrystal and two three-phase regions and therefore are of the types illustrated in the bottom row of Figure 3. References to representative systems are indicated in the figure.17−20 The phase diagrams displayed in the top two rows of Figure 3 would be expected for many of these systems at elevated temperatures.21 At still higher temperatures, one or more of the crystalline phases would melt or dissolve. Since these conditions do not meet the assumptions listed in section 2, they are not included in the current taxonomy and therefore are not illustrated in Figure 3. Solvated-Cocrystal-Containing Phase Diagrams. Phase diagrams with three solid phases including one solvated cocrystal are illustrated in Figure 4. For simplicity, the solvated cocrystal is illustrated with a 1:1:1 stoichiometry, but other stoichiometries are also possible. As in Figure 3, the phase diagrams are arranged with increasing numbers of three-phase regions in subsequent rows. Figure 4a is the simplest case, in which the two-phase regions associated with each of the crystalline phases are mutually distinct. Figure 4b illustrates the case in which the two-phase regions associated with the API and coformer meet at a eutectic but the two-phase region for the solvated cocrystal is distinct. Figure 4c−f illustrate four cases in which the solvated cocrystal participates in a pair of eutectics with either the API or the coformer. In each of these panels, there are two threephase regions that share a common edge. This edge is effectively a two-phase region of vanishing width. The vanishing width is a result of the insistence upon stoichiometric solids in the construction of the phase diagrams. If solid phase composition variability were included in the model, then these common edges would expand into two-phase regions. The fact that three-phase regions in phase diagrams are surrounded by two-phase regions is a well-known property. The same comments also apply to the neighboring three-phase regions in Figure 4g−o. Panels (g), (h), (l), and (m) in Figure 4 are similar to panels (c−f) except that the two-phase regions associated with the API and coformer also meet at a eutectic. Figure 4n illustrates the case in which the solvated cocrystal participates in two eutectics with both the API and the coformer. Incongruent variants of Figure 4n are not possible for solvated cocrystals with the 1:1:1 stoichiometry used in Figure 4 but are possible for other stoichiometries in very limited ranges of parameter space. Figure 4o is similar to Figure 4n except that the two-phase regions associated with the API and coformer also meet at a eutectic. Incongruent variants of Figure 4o are not possible for solvated cocrystals with the 1:1:1 stoichiometry used in Figure 4 but are possible for other stoichiometries in very limited ranges of parameter space. The small triangular region in Figure 4o in which the system is a single-phase solution should be noted. Increasing the magnitude of the free energy of fusion of the crystalline phases

Figure 2. Example set of minimal free energy surfaces and their projection onto a basal plane to produce the corresponding ternary phase diagram. The labels A, C, and S refer to the API, coformer, and solvent components, respectively. The free energies of the pure components are zero, as these are the chosen reference states. The free energy of mixing (eq 1) is illustrated using the yellow surface. The free energy of formation for a crystalline phase (Gf) is the value of the free energy relative to the top of the prism. Equation 2 gives the locus of solution compositions in equilibrium with a solid of specified composition (s, t, u) and free energy (Gf), which corresponds to the contact between the yellow solution surface and the green tie lines in the figure.

3. RESULTS AND DISCUSSION Cocrystal-Containing Phase Diagrams. Phase diagrams with three solid phases including one unsolvated cocrystal are illustrated in Figure 3. For simplicity, the cocrystal is illustrated with a 1:1 stoichiometry, but other stoichiometries are also possible. Figure 3a is the simplest case, in which the two-phase regions associated with each of the crystalline phases are mutually distinct. Figure 3b−e illustrate cases in which two of the two-phase regions meet at a eutectic point. Figure 3f−h illutrate cases in which the cocrystal participates in eutectics with both of its pure components. It should be noted that panels (b) and (c) of Figure 3 are topologically equivalent. They are distinguished here on the basis of the congruency of the cocrystal. For a congruent cocrystal, the cocrystal may be prepared by starting with a stoichiometric solution of its components and then removing the solvent. If a line connecting the pure solvent and the cocrystal compositions does not pass through a three-phase region, then this procedure may result in pure cocrystals as long as the cocrystal nucleates readily or a seed crystal is provided. This is called a congruent cocrystal, as illustrated in Figure 3c. For incongruent cocrystals, as illustrated in Figure 3b, the line connecting the pure solvent and the cocrystal passes through a three-phase region. In that case, removing the solvent from a stoichiometric solution yields a mixture of solid phases. Preparing a pure incongruent cocrystal phase requires a more D



Article

Figure 3. Cocrystal-containing phase diagrams arranged with increasing number of three-phase regions from top (none) to bottom (two). The labeled diagrams are (a) no three-phase regions; (b) one three-phase region bounded by the crystalline API, an incongruent crystalline cocrystal, and their mutual eutectic; (c) similar to (b) except that the cocrystal is congruent; (d) one three-phase region bounded by a congruent crystalline cocrystal, the crystalline coformer, and their mutual eutectic; (e) similar to (d) except that the cocrystal is incongruent; (f) two three-phase regions combining cases (b) and (d) above; (g) two three-phase regions combining cases (c) and (d) above, resulting in a congruent cocrystal; and (h) two three-phase regions combining cases (c) and (e) above. See the text for further descriptions of the individual diagrams.

illustrated division is the one that minimizes the free energy as illustrated in the corresponding free energy surface available in the Supporting Information. This ability to complete phase diagrams using the free energy surface as motivation is a significant benefit of constructing phase diagrams and free energy surfaces concurrently.

causes the size of this single-phase region to decrease. Once the region collapses to a point, the phase diagram becomes one of the cases illustrated in Figure 4i−k, in which three solids define the vertices of a larger three-phase region. The free energy of this three-phase region is entirely below that of the fluid free energy surface in the same composition domain. More Complex Phase Diagrams. Two examples of phase diagrams with more than three solid phases including at least one cocrystal are illustrated in Figure 5. Since the number of possible phase diagrams increases rapidly with the number of included solid phases, these are meant to serve as examples rather than a complete enumeration. Figure 5a illustrates a case in which two cocrystal forms with different stoichiometries are observed (e.g., ref 22). The illustrated stoichiometries are 1:1 and 3:2, as motivated by the reference. The phase diagram contains four crystalline phases (pure API, 3:2 cocrystal, 1:1 cocrystal, and pure coformer) and three eutectic points. Figure 5b illustrates a complex diagram with six crystalline phases, including the pure API, the solvated API, the pure coformer, the solvated coformer, the 1:1 cocrystal, and the 1:1:1 solvated cocrystal (e.g., ref 7). In the referenced publication, the phase diagram was explored along the saturation conditions. Therefore, the quadrilateral defined by the pure API, solvated API, solvated cocrystal, and cocrystal in the lower-left corner of the diagram was left unspecified. To have four phases in equilibrium in a three-component system at fixed temperature and pressure is inconsistent with the phase rule except at exceptional thermodynamic states. In Figure 5b, the quadrilateral is divided into two three-phase regions, each of which is consistent with the phase rule. This is one of two ways to divide the quadrilateral into triangular regions. The

4. CONCLUSIONS The purpose of a taxonomy is classification. In the present taxonomy, the diversity of phase diagrams is illustrated for a particular choice of crystalline phases using the free energy of formation of each phase as a parameter. Unfortunately, there is no a priori method to determine the number of crystalline phases and their compositions for a particular chemical system. Knowledge of one or more crystalline phases does not preclude the discovery of additional phases or constrain the composition of such phases. Therefore, the specification of the crystalline phases to include in a phase diagram is a nontrivial step in its classification. In order to keep the parameter space to a workable size, the solution phase was treated as an ideal mixture for the taxonomy. Precise description of a particular system would require additional parameters to model nonidealities. For relatively small values of excess solution free energy, it is anticipated that the effect on the phase diagrams would be quantitative rather than qualitative and therefore would not significantly impact the taxonomy. For larger-magnitude nonidealities there is a possibility of qualitatively different behaviors such as liquid−liquid phase separation. Since such systems would not generally be desirable for cocrystal formation, this possibility has not been included in the taxonomy. E



Article

Figure 4. Solvated-cocrystal-containing phase diagrams arranged with increasing numbers of three-phase regions from top (none) to bottom (five). The labeled diagrams are (a) no three-phase regions; (b) one three-phase region bounded by the crystalline API, the crystalline coformer, and their mutual eutectic; (c) two three-phase regions involving the crystalline API, an incongruent solvated cocrystal, and two different eutectic compositions; (d) similar to (c) except that the solvated cocrystal is congruent; (e) two three-phase regions involving the crystalline coformer, a congruent solvated cocrystal, and two different eutectic compositions; (f) similar to (e) except that the solvated cocrystal is incongruent; (g) similar to (c) except that the two-phase regions associated with the API and coformer also meet at a eutectic; (h) similar to (d) except that the two-phase regions associated with the API and coformer also meet at a eutectic; (i) three three-phase regions, including one region of equilibrium among three solids (API, coformer, and solvated cocrystal) and two equilibria among two solids and a eutectic solution; (j) similar to (i) except that the solvated cocrystal is congruent; (k) similar to (i) except that the solvated cocrystal is in equilibrium with an API-rich solution; (l) similar to (e) except that the two-phase regions associated with the API and coformer also meet at a eutectic; (m) similar to (f) except that the two-phase regions associated with the API and coformer also meet at a eutectic; (n) the solvated cocrystal participates in pairs of eutectics with both the API and the coformer; and (o) similar to (n) except that the two-phase regions associated with the API and coformer also meet at a eutectic. See the text for further descriptions of the individual diagrams.

Although each of the illustrated phase diagrams was constructed for isothermal conditions, it is interesting to consider how the diagrams evolve as functions of temperature. The solution free energy surface is already scaled by kT and therefore is fixed. The crystal free energies of formation are functions of temperature and are expected to change relative to the solution free energy. Therefore, the equilibrium loci change as the temperature is changed. For small temperature differences, the phase diagrams will generally have correspondingly small quantitative changes until a boundary between qualitatively different diagrams is reached. For instance, the single-phase triangular region seen in Figure 4o may decrease in size as a function of temperature until the diagram changes discontinuously to the type illustrated in Figure 4j, for instance. At high temperature, either the API or coformer crystal, or both, will melt or decompose. Alternatively, the cocrystal or solvated cocrystal phase may become metastable. In either case, the resulting system would no longer conform to the assumptions of the present taxonomy.

Much of the cocrystal literature addresses the phase diagrams illustrated in Figure 3f−h. These are the relatively simple cases in which there is a single cocrystal phase that forms eutectics with both the pure API and pure coformer phases. These threephase diagrams are topologically equivalent. They are distinguished in the taxonomy on the basis of whether the cocrystal is congruent (Figure 3g) or incongruent (Figure 3f,h). Since screening strategies for cocrystals are often based on seeking a donor/acceptor relationship between the API and coformer, it is not surprising that phase diagrams with a single unsolvated cocrystalline phase are the most commonly reported in the literature. In some cases there are multiple cocrystal stoichiometries, as illustrated in Figure 5a. Although 1:2, 1:1, and 2:1 are most common, other stoichiometries are also observed, such as the 3:2 ratio illustrated in Figure 5a based on the system described in ref 22. The existence of multiple stoichiometries is typically an unanticipated complication rather than the result of intentional design. F



Article

interaction leads to a complicated diagram with many crystalline phases rather than the single multicomponent crystalline phase depicted in Figure 4. Constructing the minimal free energy surface along with each of the phase diagrams has multiple benefits. First, it aids in exhaustively enumerating the distinct phase diagrams for a chosen set of crystalline phases as depicted in Figures 3 and 4 to generate a taxonomy. Second, it permits the completion of a phase diagram in cases where the experimental data are incomplete, as discussed for the phase diagram in Figure 5b. Finally, free energy surfaces serve as justifications for the topology of the loci in the ternary phase diagram, which are projections of the intersections of free energy surfaces. For these reasons, the free energy surfaces for each of the illustrated phase diagrams are provided in the Supporting Information.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.6b00791. Ternary phase diagram and free energy prism in JPEG format and an animated view of the free energy prism in MP4 format for each of the phase diagrams illustrated in the figures (ZIP) Brief derivation of eq 2 (PDF)

■

AUTHOR INFORMATION

Corresponding Author

*Tel: (765)463-0112. Fax: (765)463-4722. E-mail: richard. [email protected]. ORCID

Richard B. McClurg: 0000-0003-1342-8826 Funding Figure 5. Example phase diagrams with multiple multicomponent phases: (a) multiple cocrystal stoichiometries; (b) cocrystal, solvated cocrystal, and solvates of both the API and coformer.

The work presented in the current publication was supported entirely by SSCI, a division of Albany Molecular Research Inc. (AMRI). Notes

The solvent is a necessary component of the cocrystal structure in the solvated cocrystal phase diagrams illustrated in Figure 4. The diversity of different phase diagrams depicted in the figure depends upon small differences in the free energy of formation of the solvated cocrystalline phase relative to the free energy of formation of the API and coformer phases. The lack of examples of the phase diagrams depicted in Figure 4 may be due to the choice of screening strategies used to investigate cocrystals. Typically a solvent is chosen such that the solubilities of the API and coformer are similar in magnitude, so a congruent cocrystal (Figure 3g) is more likely. In order to identify systems with phase diagrams similar to those depicted in Figure 4, the solvent should play an active role in the solvated cocrystal structure. Complex diagrams with solvated and unsolvated cocrystal structures, solvated API and coformer phases, and multiple eutectics as illustrated in Figure 5b are the result of multiple crystalline phases with similar free energies of formation. In the example motivated by ref 7, the solvent is water and there are four multicomponent crystalline hydrate phases. Apparently there is an affinity between water and the API and coformer components that results in the incorporation of water into several of the crystal structures. This promiscuous water

The author declares no competing financial interest.

■

REFERENCES

(1) Berge, S. M.; Bighley, L. D.; Monkhouse, D. C. Pharmaceutical salts. J. Pharm. Sci. 1977, 66, 1−19. (2) Grant, D. J. W.; Higuchi, T. Solubility Behavior of Organic Compounds (Techniques of Chemistry); Wiley: New York, 1990. (3) Görbitz, C. H.; Hersleth, H.-P. Acta Crystallogr., Sect. B: Struct. Sci. 2000, 56, 526−534. (4) Schultheiss, N.; Newman, A. Pharmaceutical Cocrystals and Their Physicochemical Properties. Cryst. Growth Des. 2009, 9, 2950− 2967. (5) Chiarella, R. A.; Davey, R. J.; Peterson, M. L. Making co-crystals − the utility of ternary phase diagrams. Cryst. Growth Des. 2007, 7, 1223−1226. (6) Ainouz, A.; Authelin, J.-R.; Billot, P.; Lieberman, H. Modeling and prediction of cocrystal phase diagrams. Int. J. Pharm. 2009, 374, 82−89. (7) Jayasankar, A.; Reddy, L. S.; Bethune, S. J.; Rodriguez-Hornedo, N. Understanding and Predicting the Effect of Cocrystal Components and pH on Cocrystal Solubility. Cryst. Growth Des. 2009, 9, 889−897. (8) Thakuria, R.; Delori, A.; Jones, W.; Lipert, M. P.; Roy, L.; Rodríguez-Hornedo, N. Pharmaceutical cocrystals and poorly soluble drugs. Int. J. Pharm. 2013, 453, 101−125. G



Article

(9) van Konynenburg, P. H.; Scott, R. L. Critical Lines and Phase Equilibria in Binary Van Der Waals Mixtures. Philos. Trans. R. Soc., A 1980, 298, 495−540. (10) Keith, J. B.; Mettes, J. A.; McClurg, R. B. Molecular crystal global phase diagrams. Cryst. Growth Des. 2004, 4, 1009−1012. (11) Mettes, J. A.; Keith, J. B.; McClurg, R. B. Molecular crystal global phase diagrams. I. Method of construction. Acta Crystallogr., Sect. A: Found. Crystallogr. 2004, 60, 621−636. (12) McClurg, R. B.; Keith, J. B. Molecular crystal global phase diagrams. II. Reference lattices. Acta Crystallogr., Sect. A: Found. Crystallogr. 2010, 66, 38−49. (13) Keith, J. B.; McClurg, R. B. Molecular crystal global phase diagrams. III. Sufficient parameter space determination. Acta Crystallogr., Sect. A: Found. Crystallogr. 2010, 66, 50−63. (14) Redlich, O.; Kister, A. T. Algebraic Representation of Thermodynamic Properties and The Classification of Solutions. Ind. Eng. Chem. 1948, 40, 345−348. (15) Cibulka, I. Estimation of excess volume and density of ternary liquid mixtures of non-electrolytes from binary data. Collect. Czech. Chem. Commun. 1982, 47, 1414−1419. (16) Singh, P. P.; Nigam, R. K.; Sharma, S. P.; Aggarwal, S. Molar Excess Volumes of Ternary Mixtures of Nonelectrolytes. Fluid Phase Equilib. 1984, 18, 333−344. (17) Grossjohann, C.; Eccles, K. S.; Maguire, A. R.; Lawrence, S. E.; Tajber, L.; Corrigan, O. I.; Healy, A. M. Characterization, Solubility and Intrinsic Dissolution Behaviour of Benzamide:Dibenzyl Sulfoxide Cocrystal. Int. J. Pharm. 2012, 422, 24−32. (18) 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, 47−60. (19) Barros, G. O. F.; Tamagawa, R. E.; Santana, C. C.; Miranda, E. A. Ternary phase diagram of ketamine ((R,S)-2-(2-chlorophenyl)2methylaminocyclohexanone) in ethanol and preliminary studies aiming at Enantioselective Crystallization of S-ketamine. Braz. J. Chem. Eng. 2009, 26, 427−434. (20) Sun, X.; Yin, Q.; Ding, S.; Shen, Z.; Bao, Y.; Gong, J.; Hou, B.; Hao, H.; Wang, Y.; Wang, J.; Xie, C. Solid−Liquid Phase Equilibrium and Ternary Phase Diagrams of Ibuprofen−Nicotinamide Cocrystals in Ethanol and Ethanol/Water Mixtures at (298.15 and 313.15) K. J. Chem. Eng. Data 2015, 60, 1166−1172. (21) Rager, T.; Hilfiker, R. Application of Phase Diagrams in Cocrystal Search and Preparation. In Pharmaceutical Salts and Co-crystals; Wouters, J., Quere, L., Eds.; RSC Publishing: Cambridge, U.K., 2011; Chapter 12. (22) Croker, D. M.; Foreman, M. E.; Hogan, B. N.; Maguire, N. M.; Elcoate, C. J.; Hodnett, B. K.; Maguire, A. R.; Rasmuson, A. C.; Lawrence, S. E. Understanding the p-Toluenesulfonamide/Triphenyulphosphine Oxide Crystal Chemistry: A New 1:1 Cocrystal and Ternary Phase Diagram. Cryst. Growth Des. 2012, 12, 869−875.

H


Taxonomy of Cocrystal Ternary Phase Diagrams - Journal of Chemical

Recommend Documents