Experimental solubility of aripiprazole in supercritical carbon dioxide and modeling

The solubility of compounds in supercritical carbon dioxide (SC-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{CO}}_{2}$$\end{document}CO2) has found crucial significance in the fabrication of micro/nano-scaled drugs. In this research, the solubility of Aripiprazole was measured in SC-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{CO}}_{2}$$\end{document}CO2 at various temperatures (308–338 K) and pressures (12–30 MPa). Moreover, the experimental solubility results were correlated with several semi-empirical models (Chrastil, Bartle et al., Kumar & Johnston, Menden-Santiago & Teja, Sodeifian et al., and Jouyban et al.) as well as the modified Wilson model. The molar fraction of the drug in SC-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{CO}}_{2}$$\end{document}CO2 varied in the range of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.830\times {10}^{-6}$$\end{document}1.830×10-6 to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.036\times {10}^{-5}$$\end{document}1.036×10-5. The solubility highly depended on the operating pressure and temperature. The Chrastil (0.994), Jouyban et al. (0.993) and Sodeifian et al. (0.992) models showed the highest consistency with the obtained values. Furthermore, self-consistency tests were performed on the solubility of Aripiprazole in SC-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{CO}}_{2}$$\end{document}CO2. The approximate total enthalpy (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{\Delta H}}_{\mathrm{total}}$$\end{document}ΔHtotal), vaporization enthalpy (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{\Delta H}}_{\mathrm{vap}}$$\end{document}ΔHvap), and solubility enthalpy (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{\Delta H}}_{\mathrm{sol}}$$\end{document}ΔHsol) were also calculated.


Enthalpy of fusion H SOL
Solubility enthalpy, (Table 5) Vaporization enthalpy, (  Calculated with DSC analysis.b Calculated with Group contribution 59 .c Calculated with the Ambrose-Walton corresponding states method 53 .
Physical and critical characteristics.The solubility of APZ in SC-CO 2 was quantified by thermodynamic investigations using appropriate group participation methods.The melting point ( T m ) was determined by DSC analysis while the boiling point ( T b ), critical pressure ( P c ), and critical temperature ( T c ) were evaluated by the Marrero and Gani contribution method 59 .To calculate these features, the molecular structure of APZ was broke down to 10CH 2 , 6CH (cyclic), 2C (cyclic), 2C-CL (cyclic), 2N (cyclic), 1C-O (cyclic), 1C-NH (cyclic), 1C, and 1O (cyclic).The molar volume ( V S ) and Grain Watson 52 , sublimation pressure ( P S ), and the corresponding modes of Ambrose-Walton 53 factor (ω) were determined according to the Immirzi-Perini method 54 , as listed in Table 1.
Experimental setup and solubility assessment.The experimental setup of this device includes a CO 2 cylinder (E-1), valve (E-2), filter (E-3), refrigeration unit (E-4), high-pressure pump (E-5), air compressor (E-6), Needle valve (E-7), oven (Memmert) (E-8), equilibrium cell (E-9), back pressure valve (E-10), metering valve (E-11), collection vial (E-12), control panel (E-13), syringe (E-14), digital pressure transmitter (WIKA, Germany, code IS-0-3-2111), pressure gauge (WIKA, Germany, code EN 837-1), a digital thermometer, and 1.8-inch pipe and fittings (Fig. 1).The high-pressure system was made of stainless steel 316.In a typical process, CO 2 first passed through a 1 µm filter to be purified on its way to the refrigerator, at which, its temperature was reduced to -15 °C for liquefaction.The pressure of liquid CO 2 was then increased up to 12-30 MPa.Such a high pressure can be controlled through a reciprocating pump.APZ (1 g) and liquid CO 2 were then mixed and homogenized by a magnetic stir- rer (100 rpm) in a cell placed in an oven for 120 min.The static time, drug content, and purity were checked by some preliminary tests.At the end of the static time, 600 μL of saturated SC-CO 2 was loaded into the injection www.nature.com/scientificreports/loop through a three-valve two-position valve.By opening the injection valve, the sample collected inside the vial was released with 5 ml of methanol which had been already loaded.Subsequently, the vial was washed by the syringe pump which injected 1 ml of methanol.The drug content of the obtained sample was evaluated by a spectrophotometer at a wavelength of 254 nm.A calibration curve was also used to estimate the concentration of the solutes.A set of standard solutions were obtained through diluting the stock solutions.Drug solubility in SC-CO 2 can be calculated at various pressures and temperatures using the following equations: where n solute and n CO 2 denote the number of moles of the solute and CO 2 , respectively, C S shows the solute con- centration ( g.L −1 ) based on the calibration curve.Vs(L) and Vl(L) represent the volumes of the sampling vial (1) Table 2.The APZ solubility at distinctive operational conditions (12-30 MPa) and (308-338 K).The experimental standard deviation of the mean (SD) were obtained by SD y = s(y k )

Results and discussion
Experimental data.The solubility of APZ in SC-CO 2 was examined at different temperatures (308-338 K) and pressures (12-30 MPa).The measurements were carried out in triplicates to reduce the error.Data of APZ solubility in SC-CO 2 including its mole fraction (y), density (ρ), solubility (S), and expanded uncertainty are also presented in Table 2. Accordingly, the highest APZ mole fraction (1.036 × 10 −5 ) was detected at 338 K and 30 MPa whereas the lowest value ( 1.830 × 10 −6 ) was recorded at 338 K and 12 MPa.The solubility showed an ascending trend with increasing the pressure at high temperatures.As the pressure rises, the density of SC-CO 2 increases which enhances the strength of the solvent.The solvent density and the vapor pressure of the solution are the main factors in the solubility enhancement.Based on Fig. 2, the solubility curve showed a crossover region.Temperature generally exhibited a dual effect on drug solubility in SC-CO 2 under controlled SC-CO 2 density and drug vapor pressure.The solubility of APZ in SC-CO 2 decremented in the pressure range of 12-18 MPa by enhancing the temperature.At pressures above 18 MPa, the solubility rose with temperature elevation.The crossover region for APZ ranged from 12 to 18 MPa.At pressures lower than 18 MPa, the effect of density was predominant as the solubility increased by temperature reduction.However, at pressures above 18 MPa, solubility rose with temperature increment due to the predominance of the influence of the vapor pressure of the drug.The impact of temperature on carbon dioxide density and vapor pressure of solute was reported by several articles with similar values of the SC − CO 2 pressure crossover region for Nystatin 55 , Clonazepam 56 and famotidine 57 .These transitions can be attributed to temperature-induced density changes in carbon dioxide and vapor pressure changes in solutes.The crossover pressure was investigated in several articles, which proposed some methods to predict the crossover pressure region [58][59][60] .The crossover region varies depending on the critical properties of the solute, such as its sublimation pressure, sublimation enthalpy, partial molar enthalpy, and molar volume.Thus, the pressure range of 12-18 MPa was introduced as the crossover region for APZ drug (Fig. 2).
Semi-empirical models.Semi-empirical models such as Chrastil 49 , Bartle et al. 61 , K-J 62 , MST 63 , Sodeifian et al. 33 , and Jouyban et al. 64 were used for the correlation of the solubility of APZ.Table 3 lists the equations of the semi-empirical models.Chrastil 49 proposed an equation for the solid solutes based on the SCF density and absolute temperature ( a 2 = �H t R ) , in which, the adjustable parameter of a 2 is a function of the total heat.R shows the global gas constant and H t represents the total heat of mixing.The vaporization enthalpy ( H vap ) can be deter- mined by the model proposed by Bartle et al. 61 .According to the Hess' law, the solvation enthalpy (�H sol ) can be defined as the difference between H t and H vap .Sodeifian et al. proposed a semi-empirical model a 0 − a 5 and introduced six adjustable parameters.In 1998, K-J 62 presented a density-based semi-empirical model for the correlation of the solid solubility in SCF.They expressed the relationship of a 2 with H t through H t = a 2 R .A simple linear equation is shown by MST model for consistency of solid solubility in SCF.
Semi-empirical models of Chrastil 49 , Sodeifian et al. 33 , K-J 62 , MST 63 , Bartle et al. 33 , and Jouyban et al. 64 have three, six, three, three, three, and six parameters, respectively.The mentioned models were used from the Simulated Annealing algorithm for optimization.The adjustable parameters of the relevant statistical measures were obtained in terms of AARD% and R adj for the CO 2 -APZ binary system using the density-based models as listed in Table 4.
The average absolute relative deviation (AARD %) was used to assess the precision of the models:

Model Formula
Chrastil 49 ln s = a 0 lnρ + a 1 + a2 T Bartle et al. 61 ln Sodeifian et al. 33 ln y 2 = a 0 + (a 1 + a 2 ρ)lnρ + a3 T + a 4 ln(ρT) Jouyban et al. 64 ln y 2 = a 0 + a 1 ρ + a 2 P 2 + a 3 PT + a4T P + a 5 ln(ρ)  In the above equation, Z represents the number of adjustable parameters of each model, N t shows the number of data points in each set, and y 2 denotes the mole fraction solubility.The correlation coefficient adjusted by R adj is defined as follows: While the correlation coefficient is represented by R 2 , the number of data points in each set is shown by N. Q also denotes the number of independent variables in each equation.
The AARD% values were 7.90, 10.73, 5.90, 9. Other semi-empirical models offered acceptable predictive accuracies.The results also revealed the higher precision of the Chrastil model in predicting the solubility data with R adj =0.994.Figure 3 compares the experimental solubility with those calculated by the density-based models.
Figure 4 demonstrates the self-consistency of experimental data of APZ solubility with Chrastil, Bartle et al., MST, and K-J models.The model is acceptable in self-consistency tests if all the solubility data obtained at different temperatures are located on the 45 − degree line.The test results of the mentioned semi-empirical models suggest the consistency of the measured solubility values.
Table 5 lists the calculated enthalpy for APZ in SC-CO 2 .The Chrastil model shows the approximate total heat of 30KJ.mol−1 .Based on Bartle's model, the enthalpy of vaporization was (48.73KJ.mol−1 ) .Solvation heat ( H sol ) was equal to 18.73KJ.mol−1 based on the difference between H vap and H t .

Modified Wilson model.
Since the solid solubility in the supercritical phase is very small, we can assume to be at infinite dilution condition.Consequently, the activity coefficient of the solid solute is the one at infinite dilution ( γ ∞ 2 ) and the density of the solution is that of the pure solvent.Therefore, the solubility equation is obtained: www.nature.com/scientificreports/− H f 2 is the enthalpy of fusion and T m is the melting point temperature of the solid solute.Gibbs excess energy is defined according to the following formula for the binary system.Wilson's model has two variable parameters ( ′ 12 and ′ 21 ) which are the difference of intermolecular interaction energies of the molar volume of supercritical carbon dioxide.Moreover, ϑ 1 andϑ 2 are dependent values due to the low solubility of the solute in the SC-CO 2 where ϑ 1 andϑ 2 are the molar volumes of the SCF (expanded liquid) and the solid solute respectively.The following equation can be used to determine the activity coefficient: ϑ 1 andϑ 2 can be defined under infinite dilution conditions: ρ r is the reduced density of the solvent (SCF) equal to ρ / ρ cl , where ρ cl is its critical density and the dimen- sionless energies of interaction are as follow:   A linear equation can be defined between molar volume and reduced density to capture the effect of high pressure on the model: ′ 12 , ′ 21 , α, andβ were obtained by the model.Using the extended liquid theory, the modified Wilson model was utilized for optimization of the parameters of the model of APZ solubility in SC-CO 2 .Table 6 summarizes the parameters of the modified Wilson model ( α, β, ′ 12 , ′ 21 ).A comparison of experimental and modeled data (Fig. 5) confirmed the accuracy of the modified Wilson model.Based on Table 6, ′ 21 is smaller than ′ 12 as also reported in previous studies 27,34,50,51,65 .

Conclusion
APZ solubility was evaluated at different pressures (12, 15, 18, 21, 24, 27, Aripiprazole structure and the respective physic-chemical features.T b boiling point, T c critical point, P c critical pressure, ω acentric factor, V s solid molar volume, T temperature, P sub sublimation pressure.a

√n
. n is the number of times each experimental data was measured (n = 3, in this work).Expanded uncertainty is U = k*u combined and the relative combined standard uncertainty is defined as u combined /y = N i=1 (Pi u(xi)/xi) 2 in which u(xi)/xi is the relative standard uncertainty of each input estimate (xi) and P i is known positive or negative number having negligible uncertainties.a Standard uncertainty u are u(T) = 0.1 K; u(p) = 1 bar.Also, the relative standard uncertainties are obtained below 0.05 for mole fractions and solubility's.The value of the coverage factor k = 2 was chosen on the basis of the level of confidence of approximately 95 percent.Data from the Span-Wagner equation of state.

Figure 2 .
Figure 2. Experimental solubility of APZ in SC-CO 2 at various pressures and temperatures.(a) Solubility according to pressure and (b) solubility according to density.

Figure 3 .
Figure 3.A comparison of experimental (points) and modeled (lines) values of APZ solubility based on semiempirical models at different temperatures.
30, 5.89, and 4.39 for Chrastil, Bartle et al., K-J, MST, Sodeifian et al., and Jouyban et al., respectively.The models proposed by Jouyban et al. and Sodeifian et al. showed the best performance in predicting the solubility of APZ with respective AARD% values of 4.39 and 5.89%.Jouyban et al. model exhibited the best correlation compared to others.The linear equation of Jouyban et al. is generally more suitable for predicting the solubility of this type of drug compared to the model proposed by Bartle et al.

Figure 4 .
Figure 4.The self-consistency results obtained for four semi-empirical models.The lines suggest the linearity of the models.

Figure 5 .
Figure 5. Experimental data (point) and calculated (line) solubility of APZ in SC-CO 2 based on the modified Wilson model.
and 30 MPa) and temperatures (308, 318, 328, and 338 K).The molar fraction of APZ in SC-CO 2 varied from 1.83 × 10 −6 to 1.036 × 10 −5 .The lowest and highest molar fractions of APZ were detected at a constant temperature of 338 K and pressures of 12 and 30 MPa, respectively.Six semi-empirical models (Sodeifian et al., Jouyban et al., Chrastil, Bartle et al., MST, K-J), and an extended liquid theory (modified Wilson model) were employed for the correlation of the experimental solubility data.The precision of the models was explored in terms of AARD% and R adj .Accordingly, the modified Wilson model (AARD% = 6.82) and the semi-empirical models of Chrastil (AARD% = 7.90), Bartle et al. (AARD% = 10.73),Jouyban (AARD% = 4.39), MST (AARD% = 9.30), Kumar Johnston (AARD% = 5.90), Sodeifian et al. (AARD% = 5.89), Jouyban et al., and Sodeifian et al. with six adjustable parameters showed the best correlation among density-based models, reflecting the ability of this model to correlate solubility data.Such satisfactory correlation results of the semi-empirical models also show the self-consistency of the experimental findings.The models of Chrastil and Bartle et al. were also applied to determine the enthalpy of vaporization and solvation.

Table 1 .
The solute Schematic diagram of the SC-CO 2 solubility measurement used in this research.

Table 3 .
The semi-empirical models exploited in the present study.

Table 4 .
Diverse parameters of APZ-CO 2 binary system, as obtained using models proposed by Chrastil, Bartle et al.Kumar and Johnston, MST, Sodeifian et al. and Jouyban et al.

Table 6 .
Modified Wilson model parameters for solubility of APZ in SC-CO 2 .