1. Introduction
Cocrystals (CCs) are formulations of increasing interest to the pharmaceutical industry, as they can potentially improve the solubility and dissolution behavior, as well as the physical stability of active pharmaceutical ingredients (APIs) compared to their pure state [
1,
2,
3,
4,
5,
6]. CCs consist of an API and at least one coformer (CF) in a stoichiometric ratio. Because of the weak non-covalent interactions between the API and CF in the CC, it dissociates into its components upon dissolution.
In general, CC formation is performed by crystallization from solution, for example by cooling or by the addition of anti-solvents [
7]. Anti-solvent crystallization is a favored technique, as it offers an extended range of solvent polarity compared to single solvents [
8]. This in turn provides the possibility to control crystal properties, such as purity [
9], crystal size [
10,
11], morphology [
10], crystal size distribution [
12], agglomeration [
13,
14] and polymorphism [
15,
16,
17]. Other studies investigated the influence of solvent/anti-solvent systems on crystal nucleation, the size of the metastable zone and crystal growth during crystallization processes [
11,
16,
18,
19,
20]. Moreover, Rager and Hilfiger [
21] demonstrated that mixtures of solvents or solvent/anti-solvent favor CC formation by suppressing solvate formation. However, anti-solvent crystallization is only a reasonable alternative to cooling crystallization when the solubility of the desired CC is drastically decreased in the anti-solvent/solvent mixture compared to the pure solvent [
22].
As shown in previous studies [
23,
24,
25,
26], effective CC formation by crystallization from solution requires the knowledge of the thermodynamic phase diagram for a given system of API, CF, solvent and, if appropriate, anti-solvent. The reliable and accurate experimental investigation of these diagrams is time consuming and expensive [
25,
27,
28,
29,
30]. Therefore, several approaches were developed to determine the concentration range in an API/CF/solvent system in which stable CCs are formed [
3,
23,
30,
31,
32,
33,
34].
In most of these approaches, the CC formation is modeled as a chemical reaction of the liquid API and the liquid CF, resulting in the solid CC. The solubility of the CC can be obtained from the equilibrium constant of this reaction, the so-called solubility product [
23,
26,
35]:
In Equation (1), and are the solubility mole fractions and corresponding activity coefficients of API and CF, respectively. is the activity of these components, while the activity of the solid CC is equal to one. and correspond to the stoichiometry of API and CF in the CC. The solubility product does not depend on the solvent or solvent/anti-solvent mixture. Further, it does not depend on the concentration, but only varies with temperature. Thus, it can be calculated based on only one CC solubility data point, regardless of solvent, solvent/anti-solvent mixture or concentration.
However, in many studies, the solubility product is calculated neglecting the API and CF activity coefficients. The resulting
is shown in Equation (2).
In the literature, there exist only a few studies investigating the CC phase behavior in solvent (or solvent/anti-solvent) mixtures [
21,
36,
37,
38,
39,
40,
41]. Solely, Sheikh
et al. [
36], Wang
et al. [
39] and Lee
et al. [
37] estimated CC solubility in solvent/anti-solvent mixtures using a solubility product. However, all of them calculated
via Equation (2), neglecting the activity coefficients of the components forming the CC. Since this
is only valid for one particular CC solubility point, as well as for one particular solvent/anti-solvent mixture, it is not applicable for predictions in different solvents or solvent/anti-solvent mixtures. Sun
et al. [
40] and Nishimaru
et al. [
41] emphasized the advantage of symmetrical ternary phase diagrams in view of a simple process design for CC formation via anti-solvent crystallization. This phenomenon, characterized by similar solubilities of API and CF in the anti-solvent/solvent mixture (congruent dissolution [
24]), is not necessary, but beneficial for successful cocrystal formation [
23].
In contrast to the above-mentioned approaches, this work considers the thermodynamic non-ideality of all components in API/CF/solvent/anti-solvent systems in order to identify feasible solvent/anti-solvent mixtures for efficient CC formation. For this purpose, the activity coefficients in Equation (1) were calculated using the perturbed-chain statistical associating fluid theory (PC-SAFT). PC-SAFT was already used earlier to model and predict the solubility in binary and ternary systems [
42,
43,
44,
45,
46] and also systems exhibiting CC formation [
23,
34,
47]. In a prior study, CC solubilities in different solvents and at different temperatures could be predicted for various CC systems in high accordance with experimental data [
23]. Moreover, Ruether and Sadowski [
35], as well as Fuchs
et al. [
48] presented PC-SAFT as a powerful tool for reliable solubility predictions of APIs and API-like components in solvent mixtures.
In this work, the CC composed of nicotinamide (NA) and succinic acid (SA) was considered in the solvent/anti-solvent systems ethanol/water, ethanol/acetonitrile, as well as ethanol/ethyl acetate. According to the Food and Drug Administration, these solvents/anti-solvents may be present in APIs (Class 2 and 3 solvents) [
49]. Ethanol, water and ethyl acetate are even regarded as solvents of low toxic potential, so-called Class 3 solvents [
49].
3. Materials and Experimental Methods
3.1. Materials
NA (purity >99%) was purchased as crystalline powder from Sigma-Aldrich (Hamburg, Germany), and SA, also used as crystalline powder (99.8%), was obtained from VWR Chemicals (Darmstadt, Germany). Acetonitrile (>99.9%) and ethyl acetate (≥99.5%) were also purchased from VWR Chemicals, whereas ethanol (≥99.9%) was purchased from Merck KGaA (Darmstadt, Germany). Potassium dihydrogen phosphate (≥99%) was obtained from Sigma-Aldrich, dipotassium phosphate (99.8%) from VWR Chemicals and sodium hydroxide as pellets (≥98%) from Bernd Kraft GmbH (Duisburg, Germany). All substances were used without further purification as obtained from the manufactures. Water was filtered, deionized and distilled with a Millipore purification system.
3.2. Solubility in Solvents, Anti-Solvents and Solvent/Anti-Solvent Mixtures
Solubility measurements of NA, SA and mixtures of NA/SA were performed in ethanol, ethyl acetate, acetonitrile, as well as in ethanol/water, ethanol/acetonitrile and ethanol/ethyl acetate mixtures. The corresponding solubility experiments executed in this work are listed in
Table 1.
The solubility measurements were performed by preparation of a saturated solution of the pure solute (NA or SA) or solute mixtures (NA/SA) in the (anti-)solvent or solvent/anti-solvent mixture. The solution was mixed in a glass vessel (50 mL) using a magnetic stirrer to ensure sample equilibration. The temperature of the solution was adjusted by a heating jacket and measured by a PT100 element (accuracy of ±0.1 K). All samples were equilibrated for at least 48 h. After equilibration, samples were taken from the liquid phase and filtered (pore size 0.45 µm). To avoid nucleation during sampling, the syringes (10 mL) and needles were preheated.
The concentrations of pure NA or SA in saturated solutions of ethanol, ethyl acetate and the ethanol/ethyl acetate mixtures were determined gravimetrically.
The concentrations of NA in saturated solutions of the remaining solvents and solvent/anti-solvent mixtures—namely, acetonitrile, ethanol/water mixture (0.5/0.5 w/w) and ethanol/acetonitrile mixture (0.67/0.33 w/w)—were measured via UV-VIS spectrometry (Eppendorf BioSpectrometer®, Hamburg, Germany) at 260 nm. The calibration curve, prepared prior to the experiments, resulted in a coefficient of calibration of 0.99995.
The solubilities of SA in solvents and solvent/anti-solvent mixtures containing acetonitrile, ethanol, water or mixtures of these were determined by high-performance liquid chromatography (HPLC) from Agilent Technologies (1200 Series) and a reversed-phase column (Eclipse XDB-C18, 5 µm, 4.6 mm × 150 mm), again measuring concentrations via UV-VIS spectrometry, but here at 210 nm. The HPLC worked with a mobile phase consisting of 50 mM phosphate buffer at pH 7 and acetonitrile (gradient from 100/0 v/v to 60/40 v/v).
The concentrations of NA and SA in mixed solutions of both were determined as described above. The concentration of NA was analyzed via UV-VIS spectrometry at 260 nm, whereas that of SA was determined by HPLC and UV-VIS spectrometry at 210 nm. Samples containing ethyl acetate as solvents were dissolved in water prior to photometric analysis. For that purpose, ethyl acetate was evaporated by a vacuum concentrator (IR Micro-Cenvac NB-503CIR, N-BIOTEK Co., Ltd., Gyeonggi-do, Korea) before the remaining NA/SA mixture was dissolved in water.
Every gravimetric and photometric analysis was executed three times, and the average value is reported. Additionally, the solid phase of each saturated solution was analyzed by X-ray diffraction (XRD, Miniflex, Rigaku, Japan). The experimentally-determined solubilities, their standard deviations and the corresponding solid phases are reported in the
Supplementary Material.
3.3. Melting Temperatures of NA and SA
Besides X-ray diffraction, the solid phases of NA and SA were characterized by their temperature measured using a modulated differential scanning calorimeter (DSC). The apparatus (Q2000, TA Instruments GmbH, Eschborn, Germany) was calibrated against the melting temperature and melting enthalpy of pure indium. Samples of NA (or SA) of around 3.5 mg were heated in hermetically-sealed aluminum pans (TA Instruments GmbH) with a modulated heating rate of 2 K·min−1 to approximately 20 K above the expected melting temperature. During the measurement, the apparatus was flushed by nitrogen with a flow rate of 40 mL·min−1 to ensure an inert atmosphere. The samples were analyzed using TA Universal Analysis 2000 Software (TA Instruments GmbH). It could be ensured that every sample of NA corresponds to the polymorphic form I. Further, all samples of SA showed melting temperatures identical to that of the supplied SA, so that esterification reactions with ethanol could be excluded.
5. Conclusions
This study represents a thermodynamically-correct description of the CC solubility behavior in solvent/anti-solvent mixtures using the example system NA and SA, which form a 2:1 CC in the investigated ethanol/water, ethanol/acetonitrile and ethanol/ethyl acetate mixtures.
The CC solubility in solvents or solvent/anti-solvent mixtures was modeled using the CC solubility product and accounting for thermodynamic non-idealities. The CC solubility product was obtained from only the CC solubility data point in water. Based on this, the CC solubility could be predicted in all considered solvents, as well as in all solvent/anti-solvent mixtures with high accordance to experimental data, allowing reliably determining the concentration range in which the CC is formed.
Further, employing the Gibbs–Helmholtz equation, the CC solubility could also be predicted in solvent/anti-solvent mixtures at another temperature.
In summary, the proposed approach could be successfully applied for the identification of feasible solvent/anti-solvent mixtures for efficient CC formation.