Solubility of Ketoconazole (antifungal drug) in SC-CO2 for binary and ternary systems: measurements and empirical correlations

One of the main steps in choosing the drug nanoparticle production processes by supercritical carbon dioxide (SC-CO2) is determining the solubility of the solid solute. For this purpose, the solubility of Ketoconazole (KTZ) in the SC-CO2, binary system, as well as in the SC-CO2-menthol (cosolvent), ternary system, was measured at 308–338 K and 12–30 MPa using the static analysis method. The KTZ solubility in the SC-CO2 ranged between 0.20 × 10–6 and 8.02 × 10–5, while drug solubility in the SC-CO2 with cosolvent varied from 1.2 × 10–5 to 1.96 × 10–4. This difference indicated the significant effect of menthol cosolvent on KTZ solubility in the SC-CO2. Moreover, KTZ solubilities in the two systems were correlated by several empirical and semiempirical models. Among them, Sodeifian et al., Bian et al., MST, and Bartle et al. models can more accurately correlate experimental data for the binary system than other used models. Also, the Sodeifian and Sajadian model well fitted the solubility data of the ternary system with AARD% = 6.45, Radj = 0.995.

www.nature.com/scientificreports/ mometer, oven, microliter valve, sample collector, flow meter, 1/8" piping, and connections. Pressure quantities were recorded at the accuracy of ± 0.1 MPa using both the pressure gauge (WIKA, Germany, Code EN 837-1) and pressure transmitter. To maintain the experimental temperature, the equilibrium cell was located in a precise oven (Froilabo Model, AE-60, France), which could retain the temperature within ± 0.1 K. The amount of menthol and drug in saturator cell 1 (S1) and saturator cell 2 (S2) were 5 and 2 g, respectively. A magnetic stirrer (100 rpm) was applied to accelerate the equilibration and improve saturation of the particles in cells. The sintered filter was put on the top of the column to prevent the escape of menthol particles (as either powder or liquid droplets). In this research, the equilibrium time was considered 60 min (as determined by preliminary experiments). At the end of static time, 600 ± 0.6% µL of the saturated SC-CO 2 was depressurized into the collection vial containing 5 ml methanol. Eventually, the loop was washed with the solvent collected in the collection vial, and the final volume of the solution was adjusted to 5 mL ± 0.6%. It should be noted that the experiments were carried out in triplicates. Consequently, the solubility of KTZ was determined by measuring the absorbance at max , 220 nm (at which menthol wavelength is transparent) on the UNICO-4802 UV-Vis spectro-photometer with 1-cm pass length quartz cells. Finally, the calibration curve (with regression coefficient 0.996) was applied to obtain the medicine concentrations in the collection vial.
As presented in Tables 2 and 3, solubilities of KTZ (in the equilibrium mole fraction of the solute (y) and the grams of solute (S) per liter of SC-CO 2 with/without cosolvent) were evaluated at the pressure range of 12-30 MPa and temperature range of 308-338 K. Finally, Span-Wagner equation was used to obtain the CO 2 density 59 .

Results and discussion
Binary system. In our previous study, the reliability of the solubility setup was evaluated by determining the solubility of naphthalene and alpha-tocopherol in SC-CO 2 at different pressures and temperatures and comparing them with the corresponding data in the literature 60 . In general, the authors systematically check and calibrate the device before testing naphthalene and alpha-tocopherol solubilities in SC-CO 2 .
It should be mentioned that the mole fraction and solubility (S(g/L)) of KTZ in SC-CO 2 were measured at different temperature and pressure conditions ( Table 2). Each experimental data was measured in triplicate to enhance the data reliability. The relative standard uncertainty of the solubility data was below 0.05. The relative standard uncertainty (U s ) can be calculated by the following equation:  www.nature.com/scientificreports/ where S y k and n are the experimental standard deviation and the number of measurements of each experimental data (n = 3, in this work), respectively. y and S (g/ L) values respectively ranged between 0.20 × 10 -6 and 8.02 × 10 -4 , and 0.001 and 0.784. Finally, the greatest and least values of KTZ solubility were observed at (338 K, 30 MPa) and (338 K, 12 MPa), respectively. Figure 2a shows an increase in the solubility of KTZ with pressure increment at each isotherm. An enhancement in the density also increased the solubility at the elevated pressures. Generally, SC-CO 2 density and solute vapor pressure are the two key factors contributing to the solubility of the solute in SC-CO 2 . The solubility showed and SD(ȳ) = S(y k ) √ n respectively. 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 (P i u(x i )/x i ) 2 in which u(x i )/x i is the relative standard uncertainty of each input estimate (x i ) and P i is known positive or negative number having negligible uncertainties. y 2 and S are mole fraction of solute in binary system and solubility of solute in SC-CO 2 , respectively. 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 solubilities. The value of the coverage factor k = 2 was chosen on the basis of the level of confidence of approximately 95 percent. b Data from the Span-Wagner equation of state 62 .  www.nature.com/scientificreports/ an ascending trend with increasing density and solute vapor pressure. At pressures below the crossover region, where the influence of increased solvent density on the solute solubility dominates over decreased solute vapor pressure, the solid solute exhibited higher solubility at lower temperatures rather than higher ones. At the top of the crossover region, when temperature increased, the solubility incremented more rapidly with pressure enhancement, which might be due to the competing effects of the reduction of SC-CO 2 density and the increase of solute vapor pressure. Figure 2a presents a pressure range of 19-20 MPa that was considered as the crossover pressure area for KTZ in the binary system. In general, several studies demonstrated that the solute vapor pressure and SC-CO 2 density are the major parameters below and top of the crossover area 26,60-63 . Yamini and Moradi 1 measured KTZ solubility in SC-CO 2 at 12.2-35.5 MPa and 308-348 K considering the absorbance at max (220 nm). In the present work, the mole fraction of KTZ dissolved in SC-CO 2 (in pressure and temperature spans of 12-30 MPa and 308-338 K) was 0.20 × 10 -6 and 8.02 × 10 -5 . Their solubility data at this condition ranged from 0.7 × 10 -6 to 8.16 × 10 -5 . The mean standard deviation between their experimental data and the present work was 2%. The effects of temperature and pressure on the solubility were the same for both works. Table 3. The experimental data of KTZ solubility in SC-CO 2 -menthol based on distinct conditions. y 3 , y ' 2 and e are mole fraction of menthol, mole fraction of solute in ternary system and cosolvent effect, respectively. The experimental standard deviation of the mean (SD) were obtained by SD(ȳ) = S(y k ) √ 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  www.nature.com/scientificreports/ Ternary systems. Figure 2b and Table 3 report KTZ solubility in SC-CO 2 with cosolvent (menthol) under different pressures and temperatures. Accordingly, solubility based on the solute mole fraction (y) ranged from 1.2 × 10 -5 to 1.96 × 10 -4 . Each experimental data was measured three times to enhance the reliability of the solubility data. Figure 2b presents an increase in KTZ solubility with the pressure increment at all isotherms. The increase of density with rising the pressure led to the more powerful solvation ability of SC-CO 2 and thus enhanced the solid solubility. The largest increment in solubility with rising pressure was observed at the highest temperature, which can be assigned to the impacts of the temperatures and pressures on the solvent density and pressure of the solute vapor 10 . As stated previously, temperature influences the solvating power by two challenging factors: the solvent density and pressure of the solute vapor. Therefore, an increment in temperature will decrease the solubility below the crossover pressure area and also increased the solubility above the crossover pressure area. Finally, the crossover point in the ternary system was between 13 and 15 MPa. www.nature.com/scientificreports/ In the ternary system (solute-SC-CO 2 -cosolvent), the enhancement factor has been considered to study the cosolvent effect. This factor is the ratio of the obtained solubility of solute within the ternary system to that of the binary system. By investigating the presented results in Table 3, it can be founded out that the solubility was increased by adding menthol to SC-CO 2 . The cosolvent effect "e" was applied to better evaluate the solubility enhancement 7,64 : Table 3 presents the values of " e" in this study. The highest cosolvent effect was (61.2-fold) is related to the pressure of 12 MPa and a temperature of 338 K. Other researchers also reported the cosolvent effect in their studies. Hosseini et al. 12 , compared the solubility of clozapine and lamotrigine in SC-CO 2 (with solid cosolvent (menthol)) with the cosolvent-free condition. The solubility of clozapine showed an approximate 56-fold enhancement while that of lamotrigine was increased almost 8 times. Sabet et al. 65 measured acetaminophen solubility in SC-CO 2 with and without menthol solid cosolvent under different temperatures and pressures. As shown by the results, menthol strongly augmented acetaminophen solubility by (8.27-fold). Gupta and Thakur 66 investigated the solubility of phenytoin in SC-CO 2 . They concluded that solid solute solubility in SC-CO 2 is only 3 µmol/mol while its solubility increased to 1302 µmol/mol (at 45 °C and at 196 bar) in SC-CO 2 with menthol solid cosolvent. Notably, interactions between menthol and phenytoin resulted in a 400-fold solubility enhancement. Sodeifian and Sajadian 10 determined the solubility of letrozole under different circumstances in SC-CO 2 with and without menthol. Solid co-solvent could increase letrozole solubility up to 7.1 folds compared to the binary system (without solid cosolvent).
In general, the increase in the solubility of solids in ternary systems (CO 2 + cosolvent) can be attributed to the increase in solvent density, dipole-dipole interactions, and also hydrogen bonding between the solute and the cosolvent 67 . In this case, upon adding menthol to the cell, the density of the SCF enhanced, leading to an increment in the solubility. The polarity of SC-CO 2 can also be affected by the cosolvent. Menthol enhanced the solubility of KTZ in CO 2 due to the presence of a hydroxyl (polar) group and a hydrocarbon group (nonpolar) in the respective structures. As a result, it can be concluded that stronger attractive polar interaction and hydrogen bonding could lead to greater solubility. Also, by comparing values of e in Table 3, it can be inferred that cosolvent effects decreased with the increment of the pressure, which is compatible with the published studies 4-6,11 . Correlation of the binary system. The present study considered ten semiempirical equations for correlating KTZ solubility in SC-CO 2 , as listed in Table 4. Figure 3 depicts the outputs of the correlation at different temperatures. Then, statistical criteria were employed to investigate the abilities of semiempirical models. As a general rule, the more adjustable parameters lead to more accurate correlations. To provide a reliable accuracy criterion to compare the models with different numbers of adjustable parameters, AARD and R adj with the following equations were used 68 : So that Z represents the number of the adjustable variables for each model.
where N refers to the numbers of data points in each set. Moreover, Q stands for the numbers of the independent variables in each equation. R adj can be used to compare models with different numbers of independent variables and R 2 represents the correlation coefficient 69 .  2 and a 0 -a 5 are solubility of solute, density of SC-CO 2 , temperature, pressure, reference pressure, reference density, mole fraction in binary system and adjustable parameters, respectively.

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The energy term describing the temperature term coefficient in Chrastil, Sparks et al., and Bartle et al., models were considered to determine the heat of solvation (ΔH sol. ), the vaporization heat of the solute (ΔH vap .), and total heat (ΔH t ). The second tunable variables of Chrastil, Sparks et al., and Bartle et al., models were used to calculate ΔH t and ΔH vap , respectively. Also, ∆H sol was calculated based on the difference between ∆H vap and ∆H total . Based on Table 6, the enthalpy of KTZ dissolution in SC-CO 2 and ∆H total were 99. 32    Correlation of the ternary system. The present research assessed the correlation of KTZ solubilities in SC-CO 2 with menthol by five semiempirical models (Table 7). Menthol solubility in SC-CO 2 was reported in previous work 58 . The statistical criteria (i.e., R adj and AARD%) were applied to examine the capability of the presented models. A genetic algorithm was also used to obtain adjustable parameters. Figure 4 and Table 8 present

Conclusions
In this research, the KTZ solubility in SC-CO 2 (with and without menthol) was experimentally measured at the temperature range of 308-338 K and the pressure range of 12-30 MPa using spectrophotometric analysis. The tests were carried out in triplicates to enhance the reliability of the solubility data. Moreover, the mole fractions(y) and KTZ solubility (S (g/ L)) in SC-CO 2 (binary system) ranged between 0.001 and 0.784 and 0.2 × 10 -6 and 8.02 × 10 -5 , while the mole fractions of the drug in the SC-CO 2 with cosolvent (i.e., the ternary system) ranged in 1.2 × 10 -5 -1.96 × 10 -4 . Therefore, it can be concluded that the solubility increased in the presence of menthol. Several semi-empirical and empirical models were utilized for correlating experimental results of binary and ternary systems. Among them, Sodeifian et al. model managed to correlate the experimental data for the mentioned binary system at higher accuracy. In the case of the ternary system, the highest accuracy was provided by the Sodeifian and Sajadian model. Table 5. The correlation results of the KTZ -CO 2 system provided by semi-empirical models (AARD, R adj and a 0 -a 5 are average absolute relative deviation, adjusted correlation coefficient and adjustable parameters, respectively).  Table 7. A brief statement of the density-based models utilized in the present research (ρ 1 , T, P, P ref , y ′ 2 , y 3 and a 0 -a 6 are density of SC-CO 2 , temperature, pressure, reference pressure, mole fraction in ternary system, mole fraction of cosolvent and adjustable parameters, respectively).