Subscriber access provided by George Washington University Libraries
Article
Predicting the aqueous solubility of pharmaceutical cocrystals as function of pH and temperature Gabriele Sadowski Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/acs.cgd.6b00024 • Publication Date (Web): 30 Mar 2016 Downloaded from http://pubs.acs.org on April 5, 2016
Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.
Crystal Growth & Design is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.
Page 1 of 39
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Crystal Growth & Design
Predicting the aqueous solubility of pharmaceutical cocrystals as function of pH and temperature Linda Lange, Kristin Lehmkemper, Gabriele Sadowski* Department of Chemical and Biochemical Engineering, Laboratory of Thermodynamics, TU Dortmund University, Emil-Figge-Str. 70, D-44227 Dortmund, Germany ABSTRACT: The solubility of pharmaceutical cocrystals in aqueous solution is influenced by pH-dependent dissociation and salt formation which complicates the design of cocrystal formation and purification processes. To increase the efficiency of those processes, the aqueous solubility of pharmaceutical cocrystals was predicted in this work using PCSAFT. Modeling results and experimental data of pH-dependent solubilities were compared for the weak base nicotinamide, the weak acid succinic acid, their 2:1 cocrystal, as well as for all occurring salts at 298.15 K and 310.15 K. It was found, that the pH-dependent acid-base equilibria of nicotinamide and succinic acid directly influence the solubility of their cocrystal and their salts. By accounting for the thermodynamic non-ideality of the components in the cocrystal system, PC-SAFT is able to predict the solubility behavior of all above-mentioned components in good agreement with the experimental data.
1. INTRODUCTION The formation of pharmaceutical cocrystals (CCs) is an emerging method to meet the requirements on solubility and dissolution behavior of active pharmaceutical ingredients (APIs)1-6. These CCs are crystalline solids that consist of the API and at least one coformer (CF) with a defined stoichiometry7 in the same crystal lattice. Due to the weak interactions between the API and CF in the CC, it dissociates into its components upon dissolution. The solubility of a CC is an important property that needs to be known for both, the design of CC formulations and the corresponding formation processes, preferably performed by crystallization from solution8-12. In aqueous solutions, CC formation is often influenced by pH-dependent dissociation and salt formation of API and CF. Thus, an effective CC formation from aqueous solutions requires the knowledge of the thermodynamic phase diagram8, 13, preferentially as function of pH. For a given system of API, CF, or -if applicable- the respective salts, this diagram provides the concentration range in which stable CCs can form. However, the reliable and accurate measurement of these diagrams requires high experimental effort13-17. CC formation is feasible for components covering a wide range of ionization properties and even for non-ionizable components, whereby CCs offer a great alternative to extensively used pharmaceutical salts18-20. Usually, CC components are -like salts- electrolytes with acidic, basic, amphoteric or zwitterionic properties14, 21-24. There are many cases reported2427
where pharmaceutical CCs consist of a basic API and an acidic CF like the CC system investigated in this work. In water, dissociation of those APIs and CFs take place. Adding an acid (or a base) to a basic API (or acidic CF) leads to
a significant increase in solubility due to ionization of the respective component. This influence of pH on the solubility of APIs is a well-known phenomenon that has already been elaborated in literature28-36. Most modeling approaches for those systems are based on the Henderson-Hasselbalch (HH) equation37 that describes the solubility of an electrolyte, present as neutral and ionic species, at a certain pH on the basis of the so-called intrinsic solubility, which corresponds to the solubility of the neutral species. However, the HH equation is only describing the mass balance of neutral and ionic species and does not account for non-ideal interactions between different components. Therefore, Bergström et al.30 disadvised from using the HH equation without accounting for the strong interactions between buffer components and APIs. Avdeef et al.28 accounted for the effect of additional components on the API solubility by empirically modifying the p -value of the API. In contrast, Cassens et al.35 and Grosse-Daldrup et al.36 calculated pH-dependent API solubilities
using p -values from literature, but considering the thermodynamic non-idealities by accounting for activity coefficients.
Adjusting the pH in a solution of a basic/acidic API (or basic/acidic CF) by adding a strong base or acid may cause salt formation of the cationic species of the basic API (or anionic species of the acidic CF) with the counter ion of the pHmodifying acid (or base). By selecting a suitable counter ion (i.e. the acid or the base to change the pH) the solubility and dissolution behavior of the resulting salt can be remarkably improved38-42. Various approaches have been developed to
model the pH-dependent solubility of these salts using a so-called solubility product
the salt ions were neglected in these approaches, resulting strictly-speaking in
32, 43-47
.
. The activity coefficients of
However, Streng et al.48 and
Cassens et al.35 demonstrated that salt solubility is significantly influenced by interactions between the released
ACS Paragon Plus Environment
Crystal Growth & Design
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 2 of 39
counterions of the pH-modifying acid (or base) and the API (or CF) and therefore activity coefficients have to be considered for reliable solubility calculations. CC solubility in aqueous solutions consisting of API, CF and the pH-modifying acid or base is –as for salts- usually also
modeled via the corresponding CC solubility product . The solubility product of any complex, a salt or a CC, is described by Eq. (1)49, 50:
= ν = ν ∙ ν
(1)
Eq. (1) treats complex formation as chemical reaction of component A and component B in a liquid solution, resulting in the solid complex. In the case of a salt, A refers to the ionic API species and B refers to the counter ion, whereas for a CC, components A and B correspond to the neutral components API and CF. xi and γi in Eq. (1) are the mole fractions and activity coefficients of A and B at solubility, respectively, and ai is the activity of these components. The activity of the salt
or the CC is one. and correspond to the stoichiometric coefficients of A and B, respectively. The solubility product
does not depend on the solvent nor on concentration; it only varies with temperature. Therefore, it can be calculated
based on only one salt or CC solubility data point, regardless of solvent, concentration, and pH.
In almost all studies3, 12, 17, 51-57, the solubility product is calculated neglecting the API and CF activity coefficients,
resulting in described by Eq. (2).
=
∏ ν = = ν = ν ν ν ∏ ∏ ν
(2)
This might be appropriate for poorly-soluble solutes and if -values were obtained using activity coefficients that
refer to the infinite-dilution reference state. For highly-soluble components as considered in this study, needs to be
determined using activity coefficients that describe deviations from the pure-component reference state.
Since most APIs and CFs are electrolytes, also the CC solubility depends on pH, as already described for the salt solubility. Only a few studies exist on modeling the pH-dependent CC solubility21, 22, 58, 59. Bethune et al.21 modeled the CC solubility at one CC eutectic point using and equilibrium constants for the ionization reactions of acidic or basic APIs and
CFs. Salt formation of APIs or CFs with the pH-modifying acid and base as well as activity coefficients of all components were completely neglected. Furthermore, the predictions were limited to one temperature only. In contrast to the above-mentioned approaches, this work accounts for the thermodynamic non-ideality of all components in aqueous CC solutions using PC-SAFT for calculating the activity coefficients in Eq. (1). The PerturbedChain Statistical Associating Fluid Theory (PC-SAFT)60 was already used earlier to model and predict the activity coefficients of the neutral and ionic components involved in binary and ternary systems60-64, including those with salt35 and CC formation50, 65, 66. CC solubilities in different solvents and at different temperatures could be predicted for various CC systems in excellent agreement with experimental data50. Besides this, PC-SAFT has previously been used to model solubilities in aqueous systems as function of pH35, 36, 67-70. Fuchs et al.67 modeled the solubilities of neutral amino acids with PC-SAFT. The pH-dependent solubilities were calculated by using p -values from literature. Cassens et al.35 extended this approach by accounting for ionic interactions and API salts.
2. THEORY 2.1 Solubility calculations and dissociation equilibria The solubility of the neutral species of an API or a CF is calculated considering the thermodynamic equilibrium between a pure solid phase and the liquid solution according to71: =
1 ∆h " ∆%&, " " − #1 − $ − # − 1 − ln $* !" ! " " "
(3)
In Eq. (3), is the mole fraction of neutral component i (API or CF) in the liquid phase (the solubility), also called
intrinsic solubility. T is the temperature of the system and ! is the ideal gas constant. " and ∆h are the melting
temperature and heat of fusion of component i (API or CF), respectively. ∆%&, describes the difference in the solid and
liquid heat capacities of component i at its melting point. The activity coefficients of API or CF (referring to the purecomponent reference state) in the liquid phase depends on temperature and on the concentrations of all components in
ACS Paragon Plus Environment
Page 3 of 39
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Crystal Growth & Design
the liquid mixture. They cannot be neglected and become increasingly important at very low solubilities. They were calculated in this work by PC-SAFT. Basic or acidic APIs and CFs have functional groups, which can be ionized in aqueous solutions upon pH change. The
ionization of any acid +, is caused by dissociation into the ionized form +- and a proton that forms a hydronium ion (,. /0 ) in aqueous solution:
34 (4) +, + ,2 / ↔ +- + ,. /0 The dissociation equilibrium can be described by the dissociation constant that equals the activity product of the
different species: 6 789: 6 789: 6 789: = = 7 7; 9 7 7; 9 7 7; 9
(5)
< The commonly-used acid constants
