Cocrystal solubility

Using the carbamazepine-nicotinamide cocrystal system, a mathematical model has been developed to predict the solubility of cocrystals [41], The model predicted that the solubility of a solid cocrystal is determined by the solubility products of the reactant species and solution complexa-tion constants that could be obtained from the performance of solubility studies. In addition, graphical methods were developed to use the dependence of cocrystal solubility on ligand concentration for evaluation of the stoichiometry of the solution-phase complexes that are the precursor to the crystalline cocrystal itself. It was proposed that the dependence of cocrystal solubility on solubility product and complexation constants would aid in the design of screening protocols, and would provide guidance for systems where crystallization of the cocrystal did not take place. 

S.J. Bethune, N. Huang, A. Jayasankar, N. Rodriguez-Homedo, Understanding and predicting the effect of cocrystal components and pH on cocrystal solubility, Cryst. Growth Des. 9 (2009) 3976-3988. 

This equation predicts that addition of either cocrystal component to a solution in excess of S decreases the cocrystal solubility when the preceding conditions apply. A plot of the solubility of cocrystal A B as a function of total ligand in solution according to Eq. (9) is shown in Fig. 12. 

The transition concentration of cocrystal component can be predicted by substituting the single component crystal solubility, Sa, for the cocrystal solubility, S, in Eq. (7) and rearranging to give... 

A]x is the solubility of cocrystal A B, when measuring total A in solutions under the equilibrium conditions described in Eq. (1). By combining the above equations, the cocrystal solubility can be expressed in terms of the total ligand concentration [B]t according to... 

Eq. (22) predicts that cocrystal solubility is higher than the value calculated in the absence of solution complexation by a constant value, KuK p, the product of the complexation constant and the solubility product. In the case of 1 1 and 1 2 solution complexes the cocrystal solubility initially decreases, passes... 

Fig. 13 Solubility of CBZ NCT cocrystal (1 1) and single component crystal of CBZ(III) at 25°C as a function of total NCT concentration in ethanol, 2-propanol, and ethyl acetate. The solid lines represent the predicted solubility, according to Eq. (28) with values for Ksp and Kn in Table 5. Filled symbols are experimental cocrystal solubility values in ( ) ethanol, (a) 2-propanol, and ( ) ethyl acetate. The dashed lines represent the predicted solubility of CBZ(III) based on Kn values calculated from the cocrystal solubility analysis. Table 5. Open symbols are experimental CBZ(III) polymorph solubility values in pure solvent. (Reproduced from Ref. l)...

The cocrystal solubility curves predicted from this equation and shown in Fig. 13 are in very good agreement with the experimental solubility values. Ksp values follow the same relative order as the cocrystal solubilities ethanol > 2-propanol > ethyl acetate, whereas ATn values follow a trend inverse to the solubility of cocrystal. The small ATn value obtained in ethanol and the large standard error associated with it suggests that 1 1 complexation is negligible in this solvent. 

Fig. 15 compares the experimental and predicted cocrystal solubilities had solution complexation been neglected, according to Eq. (25). This analysis shows that 1 1 solution complexation of cocrystal components increases the solubility of a 1 1 cocrystal by a constant, which is the product of K p and ATn. Thus, when the solubility of cocrystal is known only in pure solvent, the K p estimate is useful in assessing the dependence of cocrystal solubility on ligand concentrations. This is valuable in identifying the ligand concentrations in pharmaceutical processes and formulations where cocrystal formation can occur. 

Table 5 CBZ NCT cocrystal solubility product, K p, and solution complexation constant, Tn, in organic solvents...

This equation shows that the cocrystal solubility is dependent on cocrystal Ksp and ligand /fa- A plot of (Bcocrystai) as a frmction of yields a straight line with slope = KaKsp and intercept = Ksp, as shown in Fig. 16. 

Fig. 17 shows the pH-solubility profile for cocrystal plotted according to Eq. (34) with cocrystal K p values of 1 X 10 and 1 x 10 and acidic ligand pKa = 5. The pH-solubility profile of a cocrystal with one component that is a weak acid is similar to that of a weak acid. At pH < pKa, the cocrystal solubility is at its lowest intrinsic solubility value, given by K pf-. At pH = pKa, the cocrystal solubility is 1.4 times higher, and at pH > pKa, the solubility increases exponentially. Also, increasing the K p value increases the intrinsic solubility of cocrystal as observed in Fig. 17. The K p value is characteristic of the cocrystal of an API with a specific ligand. Therefore, if multiple cocrystals exist for the same API, determination and comparison of the K p and values enables one to select the cocrystal with the desired solubility pH dependence.

The effect of pKa on cocrystal solubility, plotted using a K p = 1 X 10 and pKa values of 5 and 2, is shown in Fig. 18. This plot shows that by lowering the pKa of the acid, higher cocrystal solubilities are achieved at lower pH. 

Zocharski, P. Nehm, S. Rodriguez-Spong, B. Rodriguez-Hornedo, N. Can solubility products explain cocrystal solubility and predict crystallization conditions AAPS J. 2004, 6, Abstract R6192. 

Nevertheless, numerous key components of the necessary experimental and theoretical foundation for understanding aqueous solubility of cocrystals have been provided by Rodrfguez-Homedo and coworkers. In several seminal papers, they have brought together invaluable information on solubility products, solubility complexation, and phase-solubility diagrams in order to provide cohesive models for explaining cocrystal solubility. These models indicate, for example, that (i) the aqueous solubility of a cocrystal AB is accurately described by the solubility... 

Figure 9.4 Phase diagram of CBZ/NCT system in ethanol at 25 °C. The solid lines are CBZ (horizontal) and NCT (vertical) solubility curves, the dashed line is the CBZ/NCT cocrystal solubility curve (reproduced -with permission from Gagniere et al, ref. 27).

A higher [co-former]eu/[drug]eu ratio, for a series of co-crystals of the same drug with different co-formers, translates to higher co-crystal solubility. This simple observation will establish a rank order of cocrystal solubilities. 

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