DOI: 10.1021/cg901232h
Cocrystal Eutectic Constants and Prediction of Solubility Behavior
2010, Vol. 10 1028–1032
David J. Good and Naı´ r Rodrı´ guez-Hornedo* Department of Pharmaceutical Sciences, College of Pharmacy, University of Michigan, Ann Arbor, Michigan 48109 Received October 6, 2009; Revised Manuscript Received January 14, 2010
ABSTRACT: Cocrystal eutectic constants (Keu), the ratio of solution concentrations of cocrystal components at the eutectic point, are a fundamental indicator of phase behavior and are shown to be a function of the solubility ratio of cocrystal and drug in pure solvent. Keu is shown to depend on solution chemistry including (i) solvent, (ii) complexation, and (iii) ionization, as does the solubility of cocrystals. More than 40 eutectic constants are presented and shown to provide essential information for cocrystal synthesis, selection, and formulation.
Cocrystals are an emerging class of engineered solid forms and understanding their solution phase behavior and solubility is essential to their screening, synthesis, characterization, manufacture, and utility.1-3 Pharmaceutical cocrystals are important for improving the physicochemical and biopharmaceutical properties of drugs without changing their chemical structure. For the first time, we are showing that the eutectic solution composition of cocrystal components (drug and coformer) is defined by the solubility of cocrystal and drug in pure solvent. The cocrystal to drug solubility ratio (R) is shown to determine the excess eutectic coformer concentration and the eutectic constant (Keu), which is the ratio of solution concentrations of cocrystal components at the eutectic. The solution eutectic composition and cocrystal solubility ratio are a function of component ionization, complexation, solvent, and stoichiometry. These fundamental relationships can be applied to predict the solubility and thermodynamic stability of new cocrystals. The importance of eutectic constants has been demonstrated for the enantiomeric purification and stability of racemic compounds.4-6 However, the relationships established for racemates are not directly applicable to cocrystals where the components differ greatly in structural and chemical properties. The equilibrium equations that specify eutectic points also differ between cocrystals and racemates. We additionally seek to describe complexation and ionization effects on cocrystal eutectic and solubility behavior and include the relevant chemical equilibria. Three equations and equilibrium constants are considered to predict the cocrystal solubility, eutectic composition, and solution complexation from the eutectic of solid drug A and cocrystal AyBz where B is coformer Asolid h Asoln Ay Bz solid h yAsoln þ zBsoln Asoln þ Bsoln h ABsoln
Sdrug ¼ adrug Ksp ¼ aydrug azcoformer K11 ¼
acomplex adrug acoformer
ðIÞ ðIIÞ ðIIIÞ
where Sdrug, Ksp, and K11 are the intrinsic drug solubility in pure solvent, cocrystal solubility product, and complexation constant, respectively. Apparent K11 values have been shown as adequate quantitative descriptors of complexation for 2:1 and 1:1 cocrystals considered in this paper.7 Activity coefficients are relatively *To whom correspondence should be addressed: E-mail:
[email protected]; phone: 734-763-0101. pubs.acs.org/crystal
Published on Web 02/01/2010
constant for the dilute solutions and concentration ranges considered in this work. Thermodynamic and apparent equilibrium constants for these expressions are proportional such that any nonideal mixing of solution species does not necessitate a detailed analysis of activity coefficients as a function of composition. Combining K11, Ksp, and Sdrug gives the concentration of complex at the eutectic as ðz - yÞ
½ABsoln ¼ K11 ðKsp Sdrug Þ1=z For poorly water-soluble drugs and more soluble coformers, we consider the eutectic for solid drug and cocrystal in equilibrium with solution. This eutectic is most relevant for describing cocrystal solubility, stability, and equilibrium behavior relative to the drug. The eutectic constant (Keu) is the concentration ratio of total coformer to total drug that satisfies the equilibrium equations I-III. ½Beu ½B þ ½AB ¼ ½Aeu ½A þ ½AB 2 3 ðz - yÞ y ðKsp =Sdrug Þ1=z þ K11 ðKsp Sdrug Þ1=z 4 5 ¼ ðz - yÞ Sdrug þ K11 ðKsp Sdrug Þ1=z
Keu ¼
ð1Þ
Cocrystal Ksp and drug solubility represent the eutectic concentrations of free components. Considerations of ionization for either component can be added to this equation. For the case of a monoprotic acidic coformer and basic drug eq 1 is rewritten as ½Beu ½Bunionized þ ½Bionized þ ½AB ¼ ½Aunionized þ ½Aionized þ ½AB ½Aeu ! 2 3 Kacoformer ðz - yÞ 1=z y 1=z þ K11 ðKsp Sdrug Þ 7 1þ 6 6ðKsp =Sdrug Þ 7 ½Hþ 6 7 ! 6 7 ¼ 6 7 þ ½H ðz - yÞ 1=z 4 5 þ K11 ðKsp Sdrug Þ Sdrug 1 þ Kadrug
Keu ¼
ð2Þ þ
where [H ] is the hydrogen ion concentration and (Ka) is the dissociation constant for the acidic coformer or the conjugate acid of the basic drug. In this case high pH decreases the solubility of basic drug and increases Keu, therefore causing an increase in cocrystal solubility relative to the drug. For cases of other acidic or basic components, the reader is referred to recent publications on cocrystal ionization.8-10 Considering the case of components r 2010 American Chemical Society
Communication
Crystal Growth & Design, Vol. 10, No. 3, 2010
1029
Table 1. Cocrystals Analyzed for Solubility Behavior and Eutectic Constantsa group I I
component(s) A
component(s) B
(1) 4-hydroxybenzoic acid; (2) phenobarbital (3) 2-hydroxybenzoic acid; (4) 3-hydroxybenzoic acid; (5) 4-aminobenzoic acid acetaminophen
I II II
1,4-diketo-2,3-dimethyl-1,2,3,4-tetrahydrophthalazine 1,4-dimethyl-1,2,3,4-tetrahydroquinoxaline
II II
1-methyl-2,3-diketo-1,2,3,4-tetrahydroquinoxaline 1-methyl-2-keto-3-methoxy-1,2-dihydroquinoxaline
II
2,3-diketo-1,2,3,4-tetrahydroquinoxaline
III
III IV
(1) 2-hydroxybenzoic acid; (2) 4-hydroxybenzoic acid; (3) 2,4-dihydroxybenzoic acid; (4) 3,4-dihydroxybenzoic acid (5) 1,5-napthalenediol carbamazepine
IV IV
carbamazepine carbamazepine
IV
carbamazepine
V
sulfamethazine
stoichiometry
solvent (pH)
temp (°C)
ref
caffeine caffeine
1:1 1:1
a (
